LMFDB - Embedded newform 425.2.k.b.86.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.11
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.11

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.337793 - 0.245421i) q^{2} +(-0.235041 + 0.723382i) q^{3} +(-0.564161 + 1.73631i) q^{4} +(-0.399103 - 2.20016i) q^{5} +(0.0981377 + 0.302037i) q^{6} -3.97689 q^{7} +(0.493607 + 1.51917i) q^{8} +(1.95901 + 1.42331i) q^{9} +(-0.674779 - 0.645251i) q^{10} +(-2.31708 + 1.68345i) q^{11} +(-1.12341 - 0.816208i) q^{12} +(-5.71575 - 4.15274i) q^{13} +(-1.34336 + 0.976012i) q^{14} +(1.68536 + 0.228425i) q^{15} +(-2.41442 - 1.75418i) q^{16} +(0.309017 + 0.951057i) q^{17} +1.01105 q^{18} +(0.685684 + 2.11032i) q^{19} +(4.04532 + 0.548281i) q^{20} +(0.934733 - 2.87681i) q^{21} +(-0.369536 + 1.13732i) q^{22} +(-0.890072 + 0.646675i) q^{23} -1.21496 q^{24} +(-4.68143 + 1.75618i) q^{25} -2.94991 q^{26} +(-3.33608 + 2.42380i) q^{27} +(2.24361 - 6.90512i) q^{28} +(0.278588 - 0.857407i) q^{29} +(0.625363 - 0.336463i) q^{30} +(0.856186 + 2.63507i) q^{31} -4.44078 q^{32} +(-0.673172 - 2.07181i) q^{33} +(0.337793 + 0.245421i) q^{34} +(1.58719 + 8.74981i) q^{35} +(-3.57650 + 2.59848i) q^{36} +(-1.78061 - 1.29369i) q^{37} +(0.749535 + 0.544569i) q^{38} +(4.34745 - 3.15861i) q^{39} +(3.14542 - 1.69232i) q^{40} +(-5.30579 - 3.85488i) q^{41} +(-0.390283 - 1.20117i) q^{42} +7.33875 q^{43} +(-1.61579 - 4.97290i) q^{44} +(2.34966 - 4.87820i) q^{45} +(-0.141952 + 0.436884i) q^{46} +(0.668601 - 2.05774i) q^{47} +(1.83643 - 1.33424i) q^{48} +8.81568 q^{49} +(-1.15035 + 1.74215i) q^{50} -0.760608 q^{51} +(10.4351 - 7.58151i) q^{52} +(-3.15476 + 9.70935i) q^{53} +(-0.532051 + 1.63748i) q^{54} +(4.62862 + 4.42607i) q^{55} +(-1.96302 - 6.04157i) q^{56} -1.68773 q^{57} +(-0.116320 - 0.357997i) q^{58} +(7.55075 + 5.48594i) q^{59} +(-1.34743 + 2.79744i) q^{60} +(-8.71809 + 6.33406i) q^{61} +(0.935914 + 0.679981i) q^{62} +(-7.79079 - 5.66034i) q^{63} +(3.32877 - 2.41849i) q^{64} +(-6.85553 + 14.2330i) q^{65} +(-0.735857 - 0.534632i) q^{66} +(2.65252 + 8.16363i) q^{67} -1.82566 q^{68} +(-0.258590 - 0.795857i) q^{69} +(2.68352 + 2.56609i) q^{70} +(-0.171939 + 0.529172i) q^{71} +(-1.19526 + 3.67863i) q^{72} +(5.98037 - 4.34500i) q^{73} -0.918974 q^{74} +(-0.170061 - 3.79924i) q^{75} -4.05100 q^{76} +(9.21476 - 6.69491i) q^{77} +(0.693349 - 2.13391i) q^{78} +(2.03864 - 6.27430i) q^{79} +(-2.89587 + 6.01220i) q^{80} +(1.27561 + 3.92593i) q^{81} -2.73832 q^{82} +(3.77365 + 11.6141i) q^{83} +(4.46770 + 3.24597i) q^{84} +(1.96915 - 1.05946i) q^{85} +(2.47898 - 1.80108i) q^{86} +(0.554753 + 0.403052i) q^{87} +(-3.70117 - 2.68906i) q^{88} +(9.58289 - 6.96238i) q^{89} +(-0.403512 - 2.22447i) q^{90} +(22.7309 + 16.5150i) q^{91} +(-0.620685 - 1.91027i) q^{92} -2.10740 q^{93} +(-0.279164 - 0.859178i) q^{94} +(4.36939 - 2.35085i) q^{95} +(1.04376 - 3.21238i) q^{96} +(4.78283 - 14.7201i) q^{97} +(2.97787 - 2.16355i) q^{98} -6.93525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.337793	−	0.245421i	0.238855	−	0.173539i	−0.461918	−	0.886923i	$-0.652838\pi$
$2$	0.337793	−	0.245421i	0.238855	−	0.173539i	0.700773	+	0.713384i	$0.252838\pi$
$3$	−0.235041	+	0.723382i	−0.135701	+	0.417645i	−0.995698	−	0.0926538i	$-0.970465\pi$
$3$	−0.235041	+	0.723382i	−0.135701	+	0.417645i	0.859997	+	0.510298i	$0.170465\pi$
$4$	−0.564161	+	1.73631i	−0.282081	+	0.868155i
$5$	−0.399103	−	2.20016i	−0.178484	−	0.983943i
$5$	−0.399103	−	2.20016i	−0.178484	−	0.983943i
$6$	0.0981377	+	0.302037i	0.0400646	+	0.123306i
$7$	−3.97689			−1.50312			−0.751562	−	0.659662i	$-0.770699\pi$
$7$	−3.97689			−1.50312			−0.751562	+	0.659662i	$0.770699\pi$
$8$	0.493607	+	1.51917i	0.174517	+	0.537107i
$9$	1.95901	+	1.42331i	0.653005	+	0.474436i
$10$	−0.674779	−	0.645251i	−0.213384	−	0.204046i
$11$	−2.31708	+	1.68345i	−0.698624	+	0.507580i	−0.879484	−	0.475929i	$-0.842112\pi$
$11$	−2.31708	+	1.68345i	−0.698624	+	0.507580i	0.180860	+	0.983509i	$0.442112\pi$
$12$	−1.12341	−	0.816208i	−0.324302	−	0.235619i
$13$	−5.71575	−	4.15274i	−1.58527	−	1.15176i	−0.910328	−	0.413887i	$-0.864171\pi$
$13$	−5.71575	−	4.15274i	−1.58527	−	1.15176i	−0.674937	−	0.737875i	$-0.735829\pi$
$14$	−1.34336	+	0.976012i	−0.359029	+	0.260850i
$15$	1.68536	+	0.228425i	0.435159	+	0.0589790i
$16$	−2.41442	−	1.75418i	−0.603604	−	0.438544i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	1.01105			0.238307
$19$	0.685684	+	2.11032i	0.157307	+	0.484140i	0.998387	−	0.0567696i	$-0.0180800\pi$
$19$	0.685684	+	2.11032i	0.157307	+	0.484140i	−0.841081	+	0.540910i	$0.818080\pi$
$20$	4.04532	+	0.548281i	0.904562	+	0.122599i
$21$	0.934733	−	2.87681i	0.203975	−	0.627772i
$22$	−0.369536	+	1.13732i	−0.0787854	+	0.242477i
$23$	−0.890072	+	0.646675i	−0.185593	+	0.134841i	−0.676702	−	0.736257i	$-0.736592\pi$
$23$	−0.890072	+	0.646675i	−0.185593	+	0.134841i	0.491109	+	0.871098i	$0.336592\pi$
$24$	−1.21496			−0.248002
$25$	−4.68143	+	1.75618i	−0.936287	+	0.351236i
$26$	−2.94991			−0.578524
$27$	−3.33608	+	2.42380i	−0.642029	+	0.466461i
$28$	2.24361	−	6.90512i	0.424002	−	1.30495i
$29$	0.278588	−	0.857407i	0.0517326	−	0.159216i	−0.921853	−	0.387541i	$-0.873325\pi$
$29$	0.278588	−	0.857407i	0.0517326	−	0.159216i	0.973585	+	0.228324i	$0.0733246\pi$
$30$	0.625363	−	0.336463i	0.114175	−	0.0614294i
$31$	0.856186	+	2.63507i	0.153776	+	0.473273i	0.998035	−	0.0626624i	$-0.0199592\pi$
$31$	0.856186	+	2.63507i	0.153776	+	0.473273i	−0.844259	+	0.535935i	$0.819959\pi$
$32$	−4.44078			−0.785026
$33$	−0.673172	−	2.07181i	−0.117184	−	0.360656i
$34$	0.337793	+	0.245421i	0.0579309	+	0.0420893i
$35$	1.58719	+	8.74981i	0.268284	+	1.47899i
$36$	−3.57650	+	2.59848i	−0.596084	+	0.433080i
$37$	−1.78061	−	1.29369i	−0.292730	−	0.212681i	0.431721	−	0.902007i	$-0.357907\pi$
$37$	−1.78061	−	1.29369i	−0.292730	−	0.212681i	−0.724451	+	0.689326i	$0.757907\pi$
$38$	0.749535	+	0.544569i	0.121591	+	0.0883407i
$39$	4.34745	−	3.15861i	0.696149	−	0.505782i
$40$	3.14542	−	1.69232i	0.497334	−	0.267579i
$41$	−5.30579	−	3.85488i	−0.828625	−	0.602032i	0.0905447	−	0.995892i	$-0.471139\pi$
$41$	−5.30579	−	3.85488i	−0.828625	−	0.602032i	−0.919170	+	0.393861i	$0.871139\pi$
$42$	−0.390283	−	1.20117i	−0.0602220	−	0.185344i
$43$	7.33875			1.11915			0.559575	−	0.828780i	$-0.310965\pi$
$43$	7.33875			1.11915			0.559575	+	0.828780i	$0.310965\pi$
$44$	−1.61579	−	4.97290i	−0.243590	−	0.749693i
$45$	2.34966	−	4.87820i	0.350267	−	0.727199i
$46$	−0.141952	+	0.436884i	−0.0209297	+	0.0644151i
$47$	0.668601	−	2.05774i	0.0975254	−	0.300152i	−0.890378	−	0.455222i	$-0.849560\pi$
$47$	0.668601	−	2.05774i	0.0975254	−	0.300152i	0.987904	+	0.155069i	$0.0495601\pi$
$48$	1.83643	−	1.33424i	0.265065	−	0.192581i
$49$	8.81568			1.25938
$50$	−1.15035	+	1.74215i	−0.162684	+	0.246377i
$51$	−0.760608			−0.106506
$52$	10.4351	−	7.58151i	1.44708	−	1.05137i
$53$	−3.15476	+	9.70935i	−0.433339	+	1.33368i	0.461439	+	0.887172i	$0.347333\pi$
$53$	−3.15476	+	9.70935i	−0.433339	+	1.33368i	−0.894779	+	0.446510i	$0.852667\pi$
$54$	−0.532051	+	1.63748i	−0.0724030	+	0.222833i
$55$	4.62862	+	4.42607i	0.624123	+	0.596811i
$56$	−1.96302	−	6.04157i	−0.262320	−	0.807338i
$57$	−1.68773			−0.223545
$58$	−0.116320	−	0.357997i	−0.0152736	−	0.0470073i
$59$	7.55075	+	5.48594i	0.983024	+	0.714209i	0.958382	−	0.285488i	$-0.0921555\pi$
$59$	7.55075	+	5.48594i	0.983024	+	0.714209i	0.0246416	+	0.999696i	$0.492156\pi$
$60$	−1.34743	+	2.79744i	−0.173953	+	0.361149i
$61$	−8.71809	+	6.33406i	−1.11624	+	0.810994i	−0.983634	−	0.180175i	$-0.942333\pi$
$61$	−8.71809	+	6.33406i	−1.11624	+	0.810994i	−0.132603	+	0.991169i	$0.542333\pi$
$62$	0.935914	+	0.679981i	0.118861	+	0.0863577i
$63$	−7.79079	−	5.66034i	−0.981547	−	0.713136i
$64$	3.32877	−	2.41849i	0.416096	−	0.302312i
$65$	−6.85553	+	14.2330i	−0.850324	+	1.76538i
$66$	−0.735857	−	0.534632i	−0.0905778	−	0.0658086i
$67$	2.65252	+	8.16363i	0.324057	+	0.997346i	0.971864	+	0.235541i	$0.0756863\pi$
$67$	2.65252	+	8.16363i	0.324057	+	0.997346i	−0.647807	+	0.761804i	$0.724314\pi$
$68$	−1.82566			−0.221394
$69$	−0.258590	−	0.795857i	−0.0311305	−	0.0958099i
$70$	2.68352	+	2.56609i	0.320743	+	0.306707i
$71$	−0.171939	+	0.529172i	−0.0204053	+	0.0628012i	−0.960741	−	0.277448i	$-0.910511\pi$
$71$	−0.171939	+	0.529172i	−0.0204053	+	0.0628012i	0.940335	+	0.340249i	$0.110511\pi$
$72$	−1.19526	+	3.67863i	−0.140862	+	0.433530i
$73$	5.98037	−	4.34500i	0.699950	−	0.508543i	−0.179966	−	0.983673i	$-0.557599\pi$
$73$	5.98037	−	4.34500i	0.699950	−	0.508543i	0.879916	+	0.475130i	$0.157599\pi$
$74$	−0.918974			−0.106829
$75$	−0.170061	−	3.79924i	−0.0196369	−	0.438698i
$76$	−4.05100			−0.464682
$77$	9.21476	−	6.69491i	1.05012	−	0.762956i
$78$	0.693349	−	2.13391i	0.0785063	−	0.241618i
$79$	2.03864	−	6.27430i	0.229365	−	0.705914i	−0.768454	−	0.639905i	$-0.778974\pi$
$79$	2.03864	−	6.27430i	0.229365	−	0.705914i	0.997819	−	0.0660083i	$-0.0210264\pi$
$80$	−2.89587	+	6.01220i	−0.323768	+	0.672185i
$81$	1.27561	+	3.92593i	0.141735	+	0.436214i
$82$	−2.73832			−0.302397
$83$	3.77365	+	11.6141i	0.414212	+	1.27481i	0.912954	+	0.408063i	$0.133796\pi$
$83$	3.77365	+	11.6141i	0.414212	+	1.27481i	−0.498742	+	0.866751i	$0.666204\pi$
$84$	4.46770	+	3.24597i	0.487466	+	0.354165i
$85$	1.96915	−	1.05946i	0.213584	−	0.114914i
$86$	2.47898	−	1.80108i	0.267315	−	0.194216i
$87$	0.554753	+	0.403052i	0.0594757	+	0.0432117i
$88$	−3.70117	−	2.68906i	−0.394546	−	0.286655i
$89$	9.58289	−	6.96238i	1.01578	−	0.738011i	0.0503699	−	0.998731i	$-0.483960\pi$
$89$	9.58289	−	6.96238i	1.01578	−	0.738011i	0.965414	+	0.260720i	$0.0839600\pi$
$90$	−0.403512	−	2.22447i	−0.0425339	−	0.234480i
$91$	22.7309	+	16.5150i	2.38285	+	1.73124i
$92$	−0.620685	−	1.91027i	−0.0647109	−	0.199160i
$93$	−2.10740			−0.218527
$94$	−0.279164	−	0.859178i	−0.0287936	−	0.0886174i
$95$	4.36939	−	2.35085i	0.448290	−	0.241192i
$96$	1.04376	−	3.21238i	0.106529	−	0.327862i
$97$	4.78283	−	14.7201i	0.485623	−	1.49459i	−0.345453	−	0.938436i	$-0.612275\pi$
$97$	4.78283	−	14.7201i	0.485623	−	1.49459i	0.831076	−	0.556159i	$-0.187725\pi$
$98$	2.97787	−	2.16355i	0.300810	−	0.218551i
$99$	−6.93525			−0.697019
$100$	−0.408192	−	9.11919i	−0.0408192	−	0.911919i
$101$	−5.17775			−0.515205			−0.257603	−	0.966251i	$-0.582933\pi$
$101$	−5.17775			−0.515205			−0.257603	+	0.966251i	$0.582933\pi$
$102$	−0.256928	+	0.186669i	−0.0254396	+	0.0184830i
$103$	2.14224	−	6.59314i	0.211081	−	0.649642i	−0.788327	−	0.615256i	$-0.789053\pi$
$103$	2.14224	−	6.59314i	0.211081	−	0.649642i	0.999409	−	0.0343856i	$-0.0109474\pi$
$104$	3.48737	−	10.7330i	0.341964	−	1.05246i
$105$	−6.70251	−	0.908421i	−0.654098	−	0.0886528i
$106$	1.31722	+	4.05399i	0.127940	+	0.393758i
$107$	−15.9124			−1.53831			−0.769153	−	0.639065i	$-0.779321\pi$
$107$	−15.9124			−1.53831			−0.769153	+	0.639065i	$0.779321\pi$
$108$	−2.32639	−	7.15988i	−0.223857	−	0.688960i
$109$	9.56768	+	6.95133i	0.916418	+	0.665816i	0.942630	−	0.333840i	$-0.108345\pi$
$109$	9.56768	+	6.95133i	0.916418	+	0.665816i	−0.0262122	+	0.999656i	$0.508345\pi$
$110$	2.64976	+	0.359134i	0.252645	+	0.0342421i
$111$	1.35435	−	0.983990i	0.128549	−	0.0933962i
$112$	9.60187	+	6.97617i	0.907292	+	0.659186i
$113$	−8.41436	−	6.11339i	−0.791557	−	0.575100i	0.116868	−	0.993147i	$-0.462714\pi$
$113$	−8.41436	−	6.11339i	−0.791557	−	0.575100i	−0.908425	+	0.418048i	$0.862714\pi$
$114$	−0.570102	+	0.414204i	−0.0533950	+	0.0387937i
$115$	1.77802	+	1.70021i	0.165801	+	0.158546i
$116$	1.33156	+	0.967432i	0.123632	+	0.0898238i
$117$	−5.28662	−	16.2705i	−0.488748	−	1.50421i
$118$	3.89695			0.358743
$119$	−1.22893	−	3.78225i	−0.112656	−	0.346718i
$120$	0.484892	+	2.67310i	0.0442644	+	0.244020i
$121$	−0.864366	+	2.66024i	−0.0785787	+	0.241840i
$122$	−1.39040	+	4.27920i	−0.125881	+	0.387421i
$123$	4.03563	−	2.93206i	0.363880	−	0.264375i
$124$	−5.05833			−0.454251
$125$	5.73226	+	9.59902i	0.512709	+	0.858563i
$126$	−4.02083			−0.358204
$127$	−8.54766	+	6.21024i	−0.758482	+	0.551069i	−0.898444	−	0.439087i	$-0.855302\pi$
$127$	−8.54766	+	6.21024i	−0.758482	+	0.551069i	0.139962	+	0.990157i	$0.455302\pi$
$128$	3.27544	−	10.0808i	0.289510	−	0.891022i
$129$	−1.72491	+	5.30872i	−0.151870	+	0.467407i
$130$	1.17732	+	6.49028i	0.103257	+	0.569235i
$131$	−2.31940	−	7.13838i	−0.202647	−	0.623683i	−0.999802	−	0.0199083i	$-0.993663\pi$
$131$	−2.31940	−	7.13838i	−0.202647	−	0.623683i	0.797155	−	0.603775i	$-0.206337\pi$
$132$	3.97708			0.346161
$133$	−2.72689	−	8.39251i	−0.236451	−	0.727723i
$134$	2.89952	+	2.10663i	0.250481	+	0.181985i
$135$	6.66420	+	6.37257i	0.573563	+	0.548464i
$136$	−1.29228	+	0.938897i	−0.110812	+	0.0805098i
$137$	−7.37182	−	5.35594i	−0.629817	−	0.457589i	0.226520	−	0.974007i	$-0.427265\pi$
$137$	−7.37182	−	5.35594i	−0.629817	−	0.457589i	−0.856337	+	0.516418i	$0.827265\pi$
$138$	−0.282669	−	0.205371i	−0.0240624	−	0.0174824i
$139$	−13.1277	+	9.53783i	−1.11348	+	0.808988i	−0.983208	−	0.182491i	$-0.941584\pi$
$139$	−13.1277	+	9.53783i	−1.11348	+	0.808988i	−0.130269	+	0.991479i	$0.541584\pi$
$140$	−16.0878	−	2.18046i	−1.35967	−	0.184282i
$141$	1.33138	+	0.967307i	0.112123	+	0.0814619i
$142$	0.0717903	+	0.220948i	0.00602451	+	0.0185415i
$143$	20.2348			1.69212
$144$	−2.23314	−	6.87291i	−0.186095	−	0.572743i
$145$	−1.99762	−	0.270747i	−0.165893	−	0.0224843i
$146$	0.953774	−	2.93541i	0.0789349	−	0.242937i
$147$	−2.07204	+	6.37710i	−0.170899	+	0.525974i
$148$	3.25080	−	2.36184i	0.267214	−	0.194142i
$149$	−16.3139			−1.33648			−0.668242	−	0.743944i	$-0.732953\pi$
$149$	−16.3139			−1.33648			−0.668242	+	0.743944i	$0.732953\pi$
$150$	−0.989857	−	1.24162i	−0.0808215	−	0.101378i
$151$	−14.7651			−1.20156			−0.600782	−	0.799413i	$-0.705144\pi$
$151$	−14.7651			−1.20156			−0.600782	+	0.799413i	$0.705144\pi$
$152$	−2.86747	+	2.08334i	−0.232582	+	0.168981i
$153$	−0.748277	+	2.30296i	−0.0604946	+	0.186183i
$154$	1.46961	−	4.52298i	0.118424	−	0.364472i
$155$	5.45588	−	2.93541i	0.438227	−	0.235778i
$156$	3.03166	+	9.33049i	0.242727	+	0.747037i
$157$	−0.915656			−0.0730773			−0.0365387	−	0.999332i	$-0.511633\pi$
$157$	−0.915656			−0.0730773			−0.0365387	+	0.999332i	$0.511633\pi$
$158$	−0.851204	−	2.61974i	−0.0677181	−	0.208415i
$159$	−6.28207	−	4.56419i	−0.498200	−	0.361964i
$160$	1.77233	+	9.77043i	0.140115	+	0.772421i
$161$	3.53972	−	2.57176i	0.278969	−	0.202683i
$162$	1.39440	+	1.01309i	0.109554	+	0.0795957i
$163$	8.04635	+	5.84602i	0.630239	+	0.457895i	0.856483	−	0.516175i	$-0.172645\pi$
$163$	8.04635	+	5.84602i	0.630239	+	0.457895i	−0.226244	+	0.974071i	$0.572645\pi$
$164$	9.68660	−	7.03772i	0.756396	−	0.549554i
$165$	−4.28966	+	2.30795i	−0.333949	+	0.179674i
$166$	4.12505	+	2.99703i	0.320166	+	0.232614i
$167$	−7.22927	−	22.2494i	−0.559418	−	1.72171i	−0.683981	−	0.729500i	$-0.739753\pi$
$167$	−7.22927	−	22.2494i	−0.559418	−	1.72171i	0.124563	−	0.992212i	$-0.460247\pi$
$168$	4.83175			0.372778
$169$	11.4074	+	35.1083i	0.877492	+	2.70064i
$170$	0.405152	−	0.841147i	0.0310737	−	0.0645130i
$171$	−1.66037	+	5.11008i	−0.126971	+	0.390778i
$172$	−4.14024	+	12.7424i	−0.315690	+	0.971595i
$173$	2.57722	−	1.87246i	0.195943	−	0.142361i	−0.485488	−	0.874243i	$-0.661358\pi$
$173$	2.57722	−	1.87246i	0.195943	−	0.142361i	0.681431	+	0.731883i	$0.261358\pi$
$174$	0.286309			0.0217050
$175$	18.6176	−	6.98415i	1.40736	−	0.527952i
$176$	8.54746			0.644289
$177$	−5.74317	+	4.17265i	−0.431683	+	0.313636i
$178$	1.52832	−	4.70368i	0.114552	−	0.352556i
$179$	−5.33387	+	16.4160i	−0.398672	+	1.22699i	0.527392	+	0.849622i	$0.323170\pi$
$179$	−5.33387	+	16.4160i	−0.398672	+	1.22699i	−0.926065	+	0.377365i	$0.876830\pi$
$180$	7.14448	+	6.83183i	0.532518	+	0.509215i
$181$	−1.59236	−	4.90079i	−0.118359	−	0.364272i	0.874274	−	0.485434i	$-0.161338\pi$
$181$	−1.59236	−	4.90079i	−0.118359	−	0.364272i	−0.992633	+	0.121161i	$0.961338\pi$
$182$	11.7315			0.869594
$183$	−2.53284	−	7.79527i	−0.187233	−	0.576243i
$184$	−1.42175	−	1.03296i	−0.104813	−	0.0761512i
$185$	−2.13568	+	4.43395i	−0.157018	+	0.325990i
$186$	−0.711864	+	0.517200i	−0.0521964	+	0.0379229i
$187$	−2.31708	−	1.68345i	−0.169441	−	0.123106i
$188$	3.19568	+	2.32180i	0.233069	+	0.169334i
$189$	13.2672	−	9.63920i	0.965049	−	0.701149i
$190$	0.898999	−	1.86644i	0.0652202	−	0.135406i
$191$	−0.771681	−	0.560659i	−0.0558369	−	0.0405679i	0.559517	−	0.828819i	$-0.310987\pi$
$191$	−0.771681	−	0.560659i	−0.0558369	−	0.0405679i	−0.615354	+	0.788251i	$0.710987\pi$
$192$	0.967096	+	2.97642i	0.0697942	+	0.214804i
$193$	−11.4518			−0.824321			−0.412160	−	0.911111i	$-0.635226\pi$
$193$	−11.4518			−0.824321			−0.412160	+	0.911111i	$0.635226\pi$
$194$	−1.99700	−	6.14613i	−0.143376	−	0.441266i
$195$	−8.68453	−	8.30449i	−0.621912	−	0.594697i
$196$	−4.97346	+	15.3068i	−0.355247	+	1.09334i
$197$	−2.04479	+	6.29322i	−0.145685	+	0.448374i	−0.997099	−	0.0761221i	$-0.975746\pi$
$197$	−2.04479	+	6.29322i	−0.145685	+	0.448374i	0.851413	+	0.524496i	$0.175746\pi$
$198$	−2.34268	+	1.70205i	−0.166487	+	0.120960i
$199$	−0.800454			−0.0567427			−0.0283713	−	0.999597i	$-0.509032\pi$
$199$	−0.800454			−0.0567427			−0.0283713	+	0.999597i	$0.509032\pi$
$200$	−4.97872	−	6.24502i	−0.352049	−	0.441589i
$201$	−6.52887			−0.460511
$202$	−1.74901	+	1.27073i	−0.123060	+	0.0894080i
$203$	−1.10792	+	3.40982i	−0.0777605	+	0.239322i
$204$	0.429106	−	1.32065i	0.0300434	−	0.0924642i
$205$	−6.36382	+	13.2121i	−0.444468	+	0.922773i
$206$	−0.894460	−	2.75286i	−0.0623200	−	0.191801i
$207$	−2.66408			−0.185166
$208$	6.51558	+	20.0529i	0.451774	+	1.39042i
$209$	−5.14140	−	3.73545i	−0.355638	−	0.258386i
$210$	−2.48700	+	1.33808i	−0.171619	+	0.0923360i
$211$	4.80382	−	3.49018i	0.330708	−	0.240274i	−0.410023	−	0.912075i	$-0.634479\pi$
$211$	4.80382	−	3.49018i	0.330708	−	0.240274i	0.740731	+	0.671802i	$0.234479\pi$
$212$	−15.0787	−	10.9553i	−1.03561	−	0.752412i
$213$	−0.342381	−	0.248754i	−0.0234596	−	0.0170444i
$214$	−5.37507	+	3.90522i	−0.367433	+	0.266955i
$215$	−2.92892	−	16.1465i	−0.199750	−	1.10118i
$216$	−5.32888	−	3.87165i	−0.362584	−	0.263433i
$217$	−3.40496	−	10.4794i	−0.231144	−	0.711388i
$218$	4.93789			0.334436
$219$	1.73746	+	5.34734i	0.117406	+	0.361340i
$220$	−10.2963	+	5.53971i	−0.694178	+	0.373487i
$221$	2.18322	−	6.71927i	0.146860	−	0.451987i
$222$	0.215997	−	0.664769i	0.0144967	−	0.0446164i
$223$	−15.3742	+	11.1700i	−1.02953	+	0.748000i	−0.968215	−	0.250118i	$-0.919531\pi$
$223$	−15.3742	+	11.1700i	−1.02953	+	0.748000i	−0.0613185	+	0.998118i	$0.519531\pi$
$224$	17.6605			1.17999
$225$	−11.6706	−	3.22273i	−0.778039	−	0.214849i
$226$	−4.34266			−0.288870
$227$	−17.9481	+	13.0401i	−1.19126	+	0.865499i	−0.993397	−	0.114731i	$-0.963399\pi$
$227$	−17.9481	+	13.0401i	−1.19126	+	0.865499i	−0.197860	+	0.980230i	$0.563399\pi$
$228$	0.952152	−	2.93042i	0.0630578	−	0.194072i
$229$	8.31493	−	25.5907i	0.549466	−	1.69108i	−0.160661	−	0.987010i	$-0.551363\pi$
$229$	8.31493	−	25.5907i	0.549466	−	1.69108i	0.710127	−	0.704073i	$-0.248637\pi$
$230$	1.01787	+	0.137957i	0.0671164	+	0.00909658i
$231$	2.67713	+	8.23937i	0.176142	+	0.542111i
$232$	1.44006			0.0945445
$233$	4.33359	+	13.3374i	0.283903	+	0.873763i	0.986725	+	0.162398i	$0.0519228\pi$
$233$	4.33359	+	13.3374i	0.283903	+	0.873763i	−0.702822	+	0.711365i	$0.748077\pi$
$234$	−5.77891	−	4.19862i	−0.377779	−	0.274473i
$235$	−4.79421	−	0.649780i	−0.312740	−	0.0423870i
$236$	−13.7851	+	10.0155i	−0.897336	+	0.651953i
$237$	4.05955	+	2.94943i	0.263696	+	0.191586i
$238$	−1.34336	−	0.976012i	−0.0870774	−	0.0632654i
$239$	−3.47815	+	2.52702i	−0.224983	+	0.163460i	−0.694567	−	0.719428i	$-0.744404\pi$
$239$	−3.47815	+	2.52702i	−0.224983	+	0.163460i	0.469584	+	0.882888i	$0.344404\pi$
$240$	−3.66847	−	3.50794i	−0.236799	−	0.226436i
$241$	17.4089	+	12.6483i	1.12140	+	0.814748i	0.984421	−	0.175825i	$-0.0562593\pi$
$241$	17.4089	+	12.6483i	1.12140	+	0.814748i	0.136983	+	0.990573i	$0.456259\pi$
$242$	0.360903	+	1.11074i	0.0231997	+	0.0714013i
$243$	−15.5106			−0.995007
$244$	−6.07949	−	18.7108i	−0.389200	−	1.19783i
$245$	−3.51836	−	19.3959i	−0.224780	−	1.23916i
$246$	0.643618	−	1.98085i	0.0410356	−	0.126295i
$247$	4.84440	−	14.9095i	0.308242	−	0.948671i
$248$	−3.58049	+	2.60138i	−0.227362	+	0.165188i
$249$	−9.28839			−0.588628
$250$	4.29211	+	1.83566i	0.271457	+	0.116098i
$251$	−14.0759			−0.888462			−0.444231	−	0.895912i	$-0.646523\pi$
$251$	−14.0759			−0.888462			−0.444231	+	0.895912i	$0.646523\pi$
$252$	14.2234	−	10.3339i	0.895988	−	0.650974i
$253$	0.973716	−	2.99679i	0.0612170	−	0.188407i
$254$	−1.36321	+	4.19554i	−0.0855357	+	0.263252i
$255$	0.303561	+	1.67346i	0.0190097	+	0.104796i
$256$	1.17535	+	3.61734i	0.0734592	+	0.226084i
$257$	−5.24852			−0.327394			−0.163697	−	0.986511i	$-0.552342\pi$
$257$	−5.24852			−0.327394			−0.163697	+	0.986511i	$0.552342\pi$
$258$	0.720208	+	2.21657i	0.0448382	+	0.137998i
$259$	7.08129	+	5.14486i	0.440010	+	0.319686i
$260$	−20.8452	−	19.9330i	−1.29277	−	1.23619i
$261$	1.76611	−	1.28316i	0.109320	−	0.0794253i
$262$	−2.53538	−	1.84206i	−0.156636	−	0.113803i
$263$	10.0422	+	7.29611i	0.619231	+	0.449898i	0.852653	−	0.522478i	$-0.174992\pi$
$263$	10.0422	+	7.29611i	0.619231	+	0.449898i	−0.233422	+	0.972376i	$0.574992\pi$
$264$	2.81514	−	2.04532i	0.173260	−	0.125881i
$265$	22.6212	+	3.06596i	1.38961	+	0.188340i
$266$	−2.98082	−	2.16569i	−0.182766	−	0.132787i
$267$	2.78408	+	8.56853i	0.170383	+	0.524386i
$268$	−15.6710			−0.957261
$269$	4.63956	+	14.2791i	0.282879	+	0.870611i	0.987026	+	0.160558i	$0.0513293\pi$
$269$	4.63956	+	14.2791i	0.282879	+	0.870611i	−0.704148	+	0.710053i	$0.748671\pi$
$270$	3.81508	+	0.517075i	0.232178	+	0.0314682i
$271$	7.41546	−	22.8224i	0.450457	−	1.38636i	−0.425930	−	0.904756i	$-0.640053\pi$
$271$	7.41546	−	22.8224i	0.450457	−	1.38636i	0.876387	−	0.481608i	$-0.159947\pi$
$272$	0.922225	−	2.83832i	0.0559181	−	0.172098i
$273$	−17.2893	+	12.5614i	−1.04640	+	0.760253i
$274$	−3.80461			−0.229845
$275$	7.89078	−	11.9502i	0.475832	−	0.720623i
$276$	1.52774			0.0919592
$277$	−1.70270	+	1.23709i	−0.102305	+	0.0743293i	−0.637762	−	0.770234i	$-0.720140\pi$
$277$	−1.70270	+	1.23709i	−0.102305	+	0.0743293i	0.535456	+	0.844563i	$0.320140\pi$
$278$	−2.09366	+	6.44361i	−0.125569	+	0.386462i
$279$	−2.07323	+	6.38076i	−0.124121	+	0.382006i
$280$	−12.5090	+	6.73018i	−0.747555	+	0.402205i
$281$	−7.26298	−	22.3532i	−0.433273	−	1.33348i	−0.894846	−	0.446376i	$-0.852715\pi$
$281$	−7.26298	−	22.3532i	−0.433273	−	1.33348i	0.461572	−	0.887103i	$-0.347285\pi$
$282$	0.687128			0.0409179
$283$	−1.23767	−	3.80915i	−0.0735717	−	0.226430i	0.907508	−	0.420035i	$-0.137982\pi$
$283$	−1.23767	−	3.80915i	−0.0735717	−	0.226430i	−0.981080	+	0.193605i	$0.937982\pi$
$284$	−0.821806	−	0.597077i	−0.0487652	−	0.0354300i
$285$	0.673577	+	3.71328i	0.0398993	+	0.219956i
$286$	6.83516	−	4.96603i	0.404171	−	0.293648i
$287$	21.1006	+	15.3305i	1.24553	+	0.904928i
$288$	−8.69955	−	6.32059i	−0.512626	−	0.372444i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−0.741228	+	0.398801i	−0.0435264	+	0.0234184i
$291$	9.52405	+	6.91963i	0.558310	+	0.405636i
$292$	4.17036	+	12.8351i	0.244052	+	0.751115i
$293$	10.1222			0.591348			0.295674	−	0.955289i	$-0.404456\pi$
$293$	10.1222			0.591348			0.295674	+	0.955289i	$0.404456\pi$
$294$	0.865150	+	2.66266i	0.0504566	+	0.155289i
$295$	9.05644	−	18.8023i	0.527286	−	1.09471i
$296$	1.08641	−	3.34362i	0.0631461	−	0.194344i
$297$	3.64958	−	11.2323i	0.211770	−	0.651762i
$298$	−5.51070	+	4.00376i	−0.319226	+	0.231932i
$299$	7.77291			0.449519
$300$	6.69260	+	1.84811i	0.386397	+	0.106700i
$301$	−29.1854			−1.68222
$302$	−4.98753	+	3.62365i	−0.287000	+	0.208518i
$303$	1.21698	−	3.74549i	0.0699139	−	0.215173i
$304$	2.04634	−	6.29800i	0.117366	−	0.361215i
$305$	17.4154	+	16.6533i	0.997202	+	0.953564i
$306$	0.312431	+	0.961565i	0.0178605	+	0.0549690i
$307$	14.7232			0.840296			0.420148	−	0.907456i	$-0.361978\pi$
$307$	14.7232			0.840296			0.420148	+	0.907456i	$0.361978\pi$
$308$	6.42584	+	19.7767i	0.366146	+	1.12688i
$309$	4.26584	+	3.09932i	0.242675	+	0.176314i
$310$	1.12254	−	2.33055i	0.0637562	−	0.132366i
$311$	0.688086	−	0.499924i	0.0390178	−	0.0283481i	−0.568105	−	0.822956i	$-0.692323\pi$
$311$	0.688086	−	0.499924i	0.0390178	−	0.0283481i	0.607123	+	0.794608i	$0.292323\pi$
$312$	6.94439	+	5.04539i	0.393149	+	0.285639i
$313$	−13.0236	−	9.46223i	−0.736140	−	0.534837i	0.155360	−	0.987858i	$-0.450346\pi$
$313$	−13.0236	−	9.46223i	−0.736140	−	0.534837i	−0.891500	+	0.453021i	$0.850346\pi$
$314$	−0.309302	+	0.224721i	−0.0174549	+	0.0126817i
$315$	−9.34435	+	19.4001i	−0.526494	+	1.09307i
$316$	9.74400	+	7.07943i	0.548143	+	0.398249i
$317$	3.66113	+	11.2678i	0.205630	+	0.632863i	0.999687	+	0.0250200i	$0.00796493\pi$
$317$	3.66113	+	11.2678i	0.205630	+	0.632863i	−0.794057	+	0.607843i	$0.792035\pi$
$318$	−3.24218			−0.181813
$319$	0.797895	+	2.45567i	0.0446735	+	0.137491i
$320$	−6.64960	−	6.35861i	−0.371724	−	0.355457i
$321$	3.74006	−	11.5107i	0.208750	−	0.642465i
$322$	0.564529	−	1.73744i	0.0314600	−	0.0968238i
$323$	−1.79514	+	1.30425i	−0.0998845	+	0.0725703i
$324$	−7.53628			−0.418682
$325$	34.0509	+	9.40287i	1.88880	+	0.521577i
$326$	4.15273			0.229998
$327$	−7.27726	+	5.28724i	−0.402433	+	0.292385i
$328$	3.23723	−	9.96318i	0.178746	−	0.550125i
$329$	−2.65895	+	8.18342i	−0.146593	+	0.451166i
$330$	−0.882594	+	1.83238i	−0.0485852	+	0.100869i
$331$	−5.16685	−	15.9019i	−0.283996	−	0.874049i	−0.986698	−	0.162565i	$-0.948023\pi$
$331$	−5.16685	−	15.9019i	−0.283996	−	0.874049i	0.702702	−	0.711484i	$-0.251977\pi$
$332$	−22.2946			−1.22358
$333$	−1.64692	−	5.06871i	−0.0902508	−	0.277763i
$334$	−7.90246	−	5.74147i	−0.432403	−	0.314159i
$335$	16.9027	−	9.09411i	0.923492	−	0.496864i
$336$	−7.30327	+	5.30613i	−0.398426	+	0.289473i
$337$	−5.96445	−	4.33343i	−0.324904	−	0.236057i	0.413361	−	0.910567i	$-0.364355\pi$
$337$	−5.96445	−	4.33343i	−0.324904	−	0.236057i	−0.738265	+	0.674510i	$0.764355\pi$
$338$	12.4696	+	9.05973i	0.678259	+	0.492784i
$339$	6.40004	−	4.64990i	0.347602	−	0.252548i
$340$	0.728628	+	4.01676i	0.0395154	+	0.217839i
$341$	−6.41987	−	4.66431i	−0.347655	−	0.252586i
$342$	0.693260	+	2.13364i	0.0374872	+	0.115374i
$343$	−7.22075			−0.389884
$344$	3.62246	+	11.1488i	0.195310	+	0.601103i
$345$	−1.64781	+	0.886568i	−0.0887152	+	0.0477312i
$346$	0.411026	−	1.26501i	0.0220969	−	0.0680073i
$347$	7.51222	−	23.1203i	0.403277	−	1.24116i	−0.519048	−	0.854745i	$-0.673713\pi$
$347$	7.51222	−	23.1203i	0.403277	−	1.24116i	0.922325	−	0.386415i	$-0.126287\pi$
$348$	−1.01279	+	0.735837i	−0.0542914	+	0.0394450i
$349$	−10.4982			−0.561955			−0.280978	−	0.959714i	$-0.590659\pi$
$349$	−10.4982			−0.561955			−0.280978	+	0.959714i	$0.590659\pi$
$350$	4.57482	−	6.92833i	0.244534	−	0.370335i
$351$	29.1336			1.55504
$352$	10.2896	−	7.47584i	0.548438	−	0.398464i
$353$	1.81523	−	5.58672i	0.0966152	−	0.297351i	−0.891056	−	0.453893i	$-0.850035\pi$
$353$	1.81523	−	5.58672i	0.0966152	−	0.297351i	0.987671	+	0.156542i	$0.0500348\pi$
$354$	−0.915943	+	2.81898i	−0.0486818	+	0.149827i
$355$	1.23289	+	0.167099i	0.0654348	+	0.00886868i
$356$	6.68255	+	20.5668i	0.354175	+	1.09004i
$357$	3.02486			0.160092
$358$	2.22707	+	6.85423i	0.117705	+	0.362257i
$359$	−23.2260	−	16.8746i	−1.22582	−	0.890610i	−0.229249	−	0.973368i	$-0.573627\pi$
$359$	−23.2260	−	16.8746i	−1.22582	−	0.890610i	−0.996570	+	0.0827579i	$0.973627\pi$
$360$	8.57061	+	1.16161i	0.451711	+	0.0612224i
$361$	11.3880	−	8.27390i	0.599371	−	0.435468i
$362$	−1.74064	−	1.26465i	−0.0914861	−	0.0664685i
$363$	−1.72121	−	1.25053i	−0.0903401	−	0.0656360i
$364$	−41.4991	+	30.1509i	−2.17514	+	1.58033i
$365$	−11.9465	−	11.4237i	−0.625307	−	0.597944i
$366$	−2.76869	−	2.01157i	−0.144722	−	0.105147i
$367$	11.1957	+	34.4568i	0.584411	+	1.79863i	0.601622	+	0.798781i	$0.294521\pi$
$367$	11.1957	+	34.4568i	0.584411	+	1.79863i	−0.0172108	+	0.999852i	$0.505479\pi$
$368$	3.28339			0.171158
$369$	−4.90744	−	15.1035i	−0.255471	−	0.786259i
$370$	0.366765	+	2.02189i	0.0190672	+	0.105113i
$371$	12.5461	−	38.6130i	0.651363	−	2.00469i
$372$	1.18891	−	3.65910i	0.0616423	−	0.189716i
$373$	3.73669	−	2.71486i	0.193478	−	0.140570i	−0.486829	−	0.873497i	$-0.661846\pi$
$373$	3.73669	−	2.71486i	0.193478	−	0.140570i	0.680307	+	0.732927i	$0.261846\pi$
$374$	−1.19584			−0.0618357
$375$	−8.29107	+	1.89045i	−0.428149	+	0.0976223i
$376$	3.45608			0.178234
$377$	−5.15293	+	3.74382i	−0.265389	+	0.192817i
$378$	2.11591	−	6.51210i	0.108831	−	0.334946i
$379$	1.56329	−	4.81132i	0.0803010	−	0.247141i	−0.902844	−	0.429968i	$-0.858525\pi$
$379$	1.56329	−	4.81132i	0.0803010	−	0.247141i	0.983145	+	0.182827i	$0.0585248\pi$
$380$	1.61677	+	8.91287i	0.0829384	+	0.457221i
$381$	−2.48332	−	7.64288i	−0.127224	−	0.391557i
$382$	−0.398265			−0.0203770
$383$	11.9606	+	36.8108i	0.611156	+	1.88095i	0.447067	+	0.894500i	$0.352468\pi$
$383$	11.9606	+	36.8108i	0.611156	+	1.88095i	0.164089	+	0.986446i	$0.447532\pi$
$384$	6.52237	+	4.73878i	0.332843	+	0.241825i
$385$	−18.4075	−	17.6020i	−0.938135	−	0.897082i
$386$	−3.86834	+	2.81052i	−0.196893	+	0.143051i
$387$	14.3767	+	10.4453i	0.730810	+	0.530964i
$388$	22.8603	+	16.6090i	1.16056	+	0.843193i
$389$	−15.2742	+	11.0974i	−0.774435	+	0.562660i	−0.903304	−	0.429002i	$-0.858865\pi$
$389$	−15.2742	+	11.0974i	−0.774435	+	0.562660i	0.128869	+	0.991662i	$0.458865\pi$
$390$	−4.97166	−	0.673832i	−0.251750	−	0.0341208i
$391$	−0.890072	−	0.646675i	−0.0450129	−	0.0327038i
$392$	4.35148	+	13.3925i	0.219783	+	0.676423i
$393$	5.70893			0.287977
$394$	0.853771	+	2.62764i	0.0430124	+	0.132378i
$395$	−14.6181	−	1.98126i	−0.735517	−	0.0996879i
$396$	3.91260	−	12.0418i	0.196616	−	0.605121i
$397$	−4.23221	+	13.0254i	−0.212409	+	0.653727i	0.786919	+	0.617057i	$0.211675\pi$
$397$	−4.23221	+	13.0254i	−0.212409	+	0.653727i	−0.999327	+	0.0366701i	$0.988325\pi$
$398$	−0.270387	+	0.196448i	−0.0135533	+	0.00984705i
$399$	6.71192			0.336016
$400$	14.3836	+	3.97191i	0.719179	+	0.198595i
$401$	−36.7699			−1.83620			−0.918100	−	0.396350i	$-0.870277\pi$
$401$	−36.7699			−1.83620			−0.918100	+	0.396350i	$0.870277\pi$
$402$	−2.20540	+	1.60232i	−0.109996	+	0.0799164i
$403$	6.04901	−	18.6169i	0.301323	−	0.927376i
$404$	2.92109	−	8.99018i	0.145330	−	0.447278i
$405$	8.12858	−	4.37340i	0.403912	−	0.217316i
$406$	0.462593	+	1.42372i	0.0229581	+	0.0706578i
$407$	6.30367			0.312461
$408$	−0.375442	−	1.15549i	−0.0185871	−	0.0572054i
$409$	2.32745	+	1.69099i	0.115085	+	0.0836143i	0.643839	−	0.765161i	$-0.277341\pi$
$409$	2.32745	+	1.69099i	0.115085	+	0.0836143i	−0.528754	+	0.848775i	$0.677341\pi$
$410$	1.09287	+	6.02476i	0.0539731	+	0.297542i
$411$	5.60707	−	4.07378i	0.276576	−	0.200945i
$412$	10.2392	+	7.43920i	0.504448	+	0.366503i
$413$	−30.0285	−	21.8170i	−1.47761	−	1.07354i
$414$	−0.899907	+	0.653821i	−0.0442280	+	0.0321335i
$415$	24.0469	−	12.9379i	1.18041	−	0.635095i
$416$	25.3824	+	18.4414i	1.24447	+	0.904163i
$417$	−3.81394	−	11.7381i	−0.186770	−	0.574818i
$418$	−2.65348			−0.129786
$419$	5.27000	+	16.2194i	0.257457	+	0.792370i	0.993336	+	0.115257i	$0.0367691\pi$
$419$	5.27000	+	16.2194i	0.257457	+	0.792370i	−0.735879	+	0.677113i	$0.763231\pi$
$420$	5.35860	−	11.1251i	0.261473	−	0.542851i
$421$	11.4451	−	35.2242i	0.557798	−	1.71672i	−0.130640	−	0.991430i	$-0.541703\pi$
$421$	11.4451	−	35.2242i	0.557798	−	1.71672i	0.688438	−	0.725295i	$-0.258297\pi$
$422$	0.766132	−	2.35791i	0.0372947	−	0.114781i
$423$	4.23860	−	3.07952i	0.206088	−	0.149731i
$424$	−16.3073			−0.791955
$425$	−3.11687	−	3.90962i	−0.151190	−	0.189644i
$426$	−0.176703			−0.00856130
$427$	34.6709	−	25.1899i	1.67784	−	1.21902i
$428$	8.97714	−	27.6288i	0.433926	−	1.33549i
$429$	−4.75600	+	14.6375i	−0.229622	+	0.706704i
$430$	−4.95204	−	4.73533i	−0.238808	−	0.228358i
$431$	7.75037	+	23.8532i	0.373322	+	1.14897i	0.944604	+	0.328213i	$0.106446\pi$
$431$	7.75037	+	23.8532i	0.373322	+	1.14897i	−0.571282	+	0.820754i	$0.693554\pi$
$432$	12.3065			0.592095
$433$	4.74510	+	14.6039i	0.228035	+	0.701820i	0.997969	+	0.0636965i	$0.0202890\pi$
$433$	4.74510	+	14.6039i	0.228035	+	0.701820i	−0.769934	+	0.638123i	$0.779711\pi$
$434$	−3.72203	−	2.70421i	−0.178663	−	0.129806i
$435$	0.665376	−	1.38141i	0.0319023	−	0.0662333i
$436$	−17.4674	+	12.6908i	−0.836536	+	0.607779i
$437$	−1.97500	−	1.43492i	−0.0944770	−	0.0686416i
$438$	1.89925	+	1.37988i	0.0907496	+	0.0659334i
$439$	25.9374	−	18.8446i	1.23793	−	0.899406i	0.240467	−	0.970657i	$-0.422699\pi$
$439$	25.9374	−	18.8446i	1.23793	−	0.899406i	0.997458	+	0.0712514i	$0.0226993\pi$
$440$	−4.43922	+	9.21640i	−0.211632	+	0.439374i
$441$	17.2700	+	12.5474i	0.822383	+	0.597496i
$442$	−0.911571	−	2.80553i	−0.0433590	−	0.133445i
$443$	9.78915			0.465097			0.232548	−	0.972585i	$-0.425294\pi$
$443$	9.78915			0.465097			0.232548	+	0.972585i	$0.425294\pi$
$444$	0.944443	+	2.90670i	0.0448213	+	0.137946i
$445$	−19.1429	−	18.3052i	−0.907462	−	0.867751i
$446$	−2.45194	+	7.54630i	−0.116103	+	0.357328i
$447$	3.83443	−	11.8012i	0.181362	−	0.558175i
$448$	−13.2382	+	9.61809i	−0.625444	+	0.454412i
$449$	27.7796			1.31100			0.655500	−	0.755196i	$-0.272458\pi$
$449$	27.7796			1.31100			0.655500	+	0.755196i	$0.272458\pi$
$450$	−4.73316	+	1.77559i	−0.223123	+	0.0837019i
$451$	18.7834			0.884477
$452$	15.3618	−	11.1610i	0.722559	−	0.524970i
$453$	3.47040	−	10.6808i	0.163053	−	0.501827i
$454$	−2.86243	+	8.80967i	−0.134341	+	0.413458i
$455$	27.2637	−	56.6030i	1.27814	−	2.65359i
$456$	−0.833076	−	2.56394i	−0.0390123	−	0.120068i
$457$	15.6142			0.730404			0.365202	−	0.930928i	$-0.381000\pi$
$457$	15.6142			0.730404			0.365202	+	0.930928i	$0.381000\pi$
$458$	−3.47177	−	10.6850i	−0.162225	−	0.499278i
$459$	−3.33608	−	2.42380i	−0.155715	−	0.113133i
$460$	−3.95519	+	2.12800i	−0.184412	+	0.0992186i
$461$	2.18642	−	1.58853i	0.101832	−	0.0739852i	−0.535704	−	0.844406i	$-0.679954\pi$
$461$	2.18642	−	1.58853i	0.101832	−	0.0739852i	0.637536	+	0.770421i	$0.279954\pi$
$462$	2.92643	+	2.12617i	0.136150	+	0.0989185i
$463$	7.06469	+	5.13280i	0.328324	+	0.238542i	0.739719	−	0.672916i	$-0.234958\pi$
$463$	7.06469	+	5.13280i	0.328324	+	0.238542i	−0.411395	+	0.911457i	$0.634958\pi$
$464$	−2.17667	+	1.58144i	−0.101049	+	0.0734167i
$465$	0.841069	+	4.63663i	0.0390037	+	0.215018i
$466$	4.73713	+	3.44173i	0.219443	+	0.159435i
$467$	7.97800	+	24.5537i	0.369178	+	1.13621i	0.947323	+	0.320279i	$0.103777\pi$
$467$	7.97800	+	24.5537i	0.369178	+	1.13621i	−0.578146	+	0.815934i	$0.696223\pi$
$468$	31.2332			1.44376
$469$	−10.5488	−	32.4659i	−0.487098	−	1.49913i
$470$	−1.77892	+	0.957106i	−0.0820553	+	0.0441480i
$471$	0.215217	−	0.662369i	0.00991666	−	0.0305203i
$472$	−4.60696	+	14.1788i	−0.212052	+	0.652630i
$473$	−17.0044	+	12.3544i	−0.781865	+	0.568058i
$474$	2.09514			0.0962328
$475$	−6.91609	−	8.67513i	−0.317332	−	0.398042i
$476$	7.26047			0.332783
$477$	−19.9996	+	14.5306i	−0.915719	+	0.665309i
$478$	−0.554709	+	1.70722i	−0.0253718	+	0.0780864i
$479$	−8.83960	+	27.2055i	−0.403892	+	1.24305i	0.517926	+	0.855426i	$0.326704\pi$
$479$	−8.83960	+	27.2055i	−0.403892	+	1.24305i	−0.921817	+	0.387625i	$0.873296\pi$
$480$	−7.48432	−	1.01438i	−0.341611	−	0.0463001i
$481$	4.80518	+	14.7888i	0.219097	+	0.674312i
$482$	8.98474			0.409244
$483$	1.02838	+	3.16504i	0.0467931	+	0.144014i
$484$	−4.13137	−	3.00162i	−0.187790	−	0.136437i
$485$	−34.2954	−	4.64820i	−1.55727	−	0.211064i
$486$	−5.23937	+	3.80663i	−0.237663	+	0.172672i
$487$	−16.5086	−	11.9942i	−0.748076	−	0.543509i	0.147154	−	0.989114i	$-0.452989\pi$
$487$	−16.5086	−	11.9942i	−0.748076	−	0.543509i	−0.895230	+	0.445604i	$0.852989\pi$
$488$	−13.9258	−	10.1177i	−0.630392	−	0.458007i
$489$	−6.12012	+	4.44653i	−0.276762	+	0.201079i
$490$	−5.94864	−	5.68832i	−0.268732	−	0.256972i
$491$	12.2305	+	8.88598i	0.551955	+	0.401019i	0.828506	−	0.559980i	$-0.189191\pi$
$491$	12.2305	+	8.88598i	0.551955	+	0.401019i	−0.276551	+	0.960999i	$0.589191\pi$
$492$	2.81421	+	8.66126i	0.126875	+	0.390480i
$493$	0.901531			0.0406029
$494$	−2.02270	−	6.22524i	−0.0910058	−	0.280087i
$495$	2.76788	+	15.2587i	0.124407	+	0.685827i
$496$	2.55519	−	7.86406i	0.114731	−	0.353107i
$497$	0.683781	−	2.10446i	0.0306718	−	0.0943980i
$498$	−3.13755	+	2.27956i	−0.140597	+	0.102150i
$499$	32.0732			1.43580			0.717898	−	0.696148i	$-0.245104\pi$
$499$	32.0732			1.43580			0.717898	+	0.696148i	$0.245104\pi$
$500$	−19.9008	+	4.53758i	−0.889991	+	0.202927i
$501$	17.7940			0.794977
$502$	−4.75473	+	3.45451i	−0.212214	+	0.154182i
$503$	−7.04353	+	21.6778i	−0.314055	+	0.966563i	0.662086	+	0.749428i	$0.269671\pi$
$503$	−7.04353	+	21.6778i	−0.314055	+	0.966563i	−0.976141	+	0.217135i	$0.930329\pi$
$504$	4.75341	−	14.6295i	0.211734	−	0.651650i
$505$	2.06645	+	11.3919i	0.0919560	+	0.506933i
$506$	−0.406560	−	1.25126i	−0.0180738	−	0.0556254i
$507$	−28.0779			−1.24698
$508$	−5.96064	−	18.3450i	−0.264461	−	0.813926i
$509$	−2.42422	−	1.76130i	−0.107452	−	0.0780682i	0.532762	−	0.846265i	$-0.321154\pi$
$509$	−2.42422	−	1.76130i	−0.107452	−	0.0780682i	−0.640214	+	0.768197i	$0.721154\pi$
$510$	0.513243	+	0.490783i	0.0227268	+	0.0217322i
$511$	−23.7833	+	17.2796i	−1.05211	+	0.764404i
$512$	18.4352	+	13.3940i	0.814729	+	0.591935i
$513$	−7.40249	−	5.37822i	−0.326828	−	0.237454i
$514$	−1.77291	+	1.28810i	−0.0781998	+	0.0568154i
$515$	−15.3610	−	2.08194i	−0.676885	−	0.0917413i
$516$	−8.24446	−	5.98995i	−0.362942	−	0.263693i
$517$	1.91491	+	5.89350i	0.0842178	+	0.259196i
$518$	3.65466			0.160577
$519$	0.748752	+	2.30442i	0.0328666	+	0.101153i
$520$	−25.0062	−	3.38920i	−1.09659	−	0.148626i
$521$	−2.61213	+	8.03932i	−0.114440	+	0.352209i	−0.991830	−	0.127569i	$-0.959283\pi$
$521$	−2.61213	+	8.03932i	−0.114440	+	0.352209i	0.877390	+	0.479778i	$0.159283\pi$
$522$	0.281667	−	0.866881i	0.0123282	−	0.0379423i
$523$	−5.21118	+	3.78614i	−0.227869	+	0.165556i	−0.695862	−	0.718176i	$-0.744977\pi$
$523$	−5.21118	+	3.78614i	−0.227869	+	0.165556i	0.467993	+	0.883732i	$0.344977\pi$
$524$	13.7030			0.598617
$525$	0.676314	+	15.1092i	0.0295168	+	0.659418i
$526$	5.18281			0.225981
$527$	−2.24153	+	1.62856i	−0.0976424	+	0.0709413i
$528$	−2.00900	+	6.18307i	−0.0874306	+	0.269084i
$529$	−6.73335	+	20.7231i	−0.292754	+	0.901005i
$530$	8.39373	−	4.51606i	0.364600	−	0.196165i
$531$	6.98385	+	21.4941i	0.303073	+	0.932763i
$532$	16.1104			0.698475
$533$	14.3183	+	44.0671i	0.620194	+	1.90876i
$534$	3.04334	+	2.21111i	0.131698	+	0.0956843i
$535$	6.35066	+	35.0098i	0.274563	+	1.51360i
$536$	−11.0926	+	8.05925i	−0.479128	+	0.348107i
$537$	−10.6213	−	7.71685i	−0.458344	−	0.333007i
$538$	5.07159	+	3.68473i	0.218652	+	0.158860i
$539$	−20.4266	+	14.8408i	−0.879835	+	0.639238i
$540$	−14.8244	+	7.97596i	−0.637943	+	0.343231i
$541$	29.8911	+	21.7172i	1.28512	+	0.933694i	0.999695	−	0.0247074i	$-0.00786541\pi$
$541$	29.8911	+	21.7172i	1.28512	+	0.933694i	0.285425	+	0.958401i	$0.407865\pi$
$542$	−3.09621	−	9.52915i	−0.132994	−	0.409312i
$543$	3.91941			0.168198
$544$	−1.37228	−	4.22343i	−0.0588358	−	0.181078i
$545$	11.4756	−	23.8247i	0.491559	−	1.02054i
$546$	−2.75737	+	8.48633i	−0.118005	+	0.363181i
$547$	−4.46750	+	13.7496i	−0.191017	+	0.587889i	0.808983	+	0.587832i	$0.200018\pi$
$547$	−4.46750	+	13.7496i	−0.191017	+	0.587889i	−1.00000		5.72653e-5i	$0.999982\pi$
$548$	13.4585	−	9.77816i	0.574918	−	0.417702i
$549$	−26.0942			−1.11367
$550$	−0.267373	−	5.97324i	−0.0114008	−	0.254700i
$551$	2.00043			0.0852210
$552$	1.08140	−	0.785682i	0.0460274	−	0.0334408i
$553$	−8.10746	+	24.9522i	−0.344764	+	1.06108i
$554$	−0.271554	+	0.835757i	−0.0115372	+	0.0355079i
$555$	−2.70546	−	2.58707i	−0.114840	−	0.109815i
$556$	−9.15449	−	28.1746i	−0.388237	−	1.19487i
$557$	11.9159			0.504894			0.252447	−	0.967611i	$-0.418765\pi$
$557$	11.9159			0.504894			0.252447	+	0.967611i	$0.418765\pi$
$558$	0.865647	+	2.66419i	0.0366457	+	0.112784i
$559$	−41.9465	−	30.4759i	−1.77415	−	1.28899i
$560$	11.5166	−	23.9099i	0.486664	−	1.01038i
$561$	1.76239	−	1.28045i	0.0744080	−	0.0540606i
$562$	−7.93931	−	5.76825i	−0.334900	−	0.243319i
$563$	−18.4662	−	13.4165i	−0.778259	−	0.565438i	0.126197	−	0.992005i	$-0.459723\pi$
$563$	−18.4662	−	13.4165i	−0.778259	−	0.565438i	−0.904456	+	0.426567i	$0.859723\pi$
$564$	−2.43066	+	1.76598i	−0.102349	+	0.0743611i
$565$	−10.0923	+	20.9528i	−0.424585	+	0.881493i
$566$	−1.35292	−	0.982952i	−0.0568674	−	0.0413166i
$567$	−5.07297	−	15.6130i	−0.213045	−	0.655684i
$568$	−0.888772			−0.0372920
$569$	−12.0454	−	37.0718i	−0.504967	−	1.55413i	−0.800825	−	0.598898i	$-0.795606\pi$
$569$	−12.0454	−	37.0718i	−0.504967	−	1.55413i	0.295858	−	0.955232i	$-0.404394\pi$
$570$	1.13884	+	1.08901i	0.0477010	+	0.0456135i
$571$	5.37442	−	16.5408i	0.224913	−	0.692210i	−0.773388	−	0.633933i	$-0.781439\pi$
$571$	5.37442	−	16.5408i	0.224913	−	0.692210i	0.998300	−	0.0582767i	$-0.0185606\pi$
$572$	−11.4157	+	35.1339i	−0.477314	+	1.46902i
$573$	0.586947	−	0.426442i	0.0245201	−	0.0178149i
$574$	10.8900			0.454541
$575$	3.03114	−	4.59050i	0.126407	−	0.191437i
$576$	9.96337			0.415140
$577$	30.1055	−	21.8729i	1.25331	−	0.910582i	0.254900	−	0.966968i	$-0.417958\pi$
$577$	30.1055	−	21.8729i	1.25331	−	0.910582i	0.998409	+	0.0563855i	$0.0179576\pi$
$578$	−0.129025	+	0.397099i	−0.00536674	+	0.0165171i
$579$	2.69165	−	8.28404i	0.111861	−	0.344273i
$580$	1.59708	−	3.31574i	0.0663152	−	0.137679i
$581$	−15.0074	−	46.1881i	−0.622612	−	1.91620i
$582$	4.91537			0.203749
$583$	−9.03543	−	27.8082i	−0.374209	−	1.15170i
$584$	9.55273	+	6.94047i	0.395295	+	0.287199i
$585$	−33.6880	+	18.1250i	−1.39283	+	0.749379i
$586$	3.41922	−	2.48421i	0.141247	−	0.102622i
$587$	28.2081	+	20.4943i	1.16427	+	0.845892i	0.990312	−	0.138861i	$-0.0443440\pi$
$587$	28.2081	+	20.4943i	1.16427	+	0.845892i	0.173959	+	0.984753i	$0.444344\pi$
$588$	−9.90366	−	7.19543i	−0.408420	−	0.296734i
$589$	−4.97376	+	3.61365i	−0.204940	+	0.148898i
$590$	−1.55528	−	8.57393i	−0.0640300	−	0.352983i
$591$	−4.07179	−	2.95833i	−0.167491	−	0.121689i
$592$	2.02977	+	6.24700i	0.0834232	+	0.256750i
$593$	−44.5530			−1.82957			−0.914786	−	0.403938i	$-0.867641\pi$
$593$	−44.5530			−1.82957			−0.914786	+	0.403938i	$0.867641\pi$
$594$	−1.52383	−	4.68986i	−0.0625234	−	0.192427i
$595$	−7.83110	+	4.21335i	−0.321044	+	0.172730i
$596$	9.20366	−	28.3259i	0.376996	−	1.16028i
$597$	0.188140	−	0.579034i	0.00770004	−	0.0236983i
$598$	2.62563	−	1.90763i	0.107370	−	0.0780089i
$599$	−5.51193			−0.225211			−0.112606	−	0.993640i	$-0.535920\pi$
$599$	−5.51193			−0.225211			−0.112606	+	0.993640i	$0.535920\pi$
$600$	5.68774	−	2.13368i	0.232201	−	0.0871073i
$601$	24.9576			1.01804			0.509022	−	0.860754i	$-0.330007\pi$
$601$	24.9576			1.01804			0.509022	+	0.860754i	$0.330007\pi$
$602$	−9.85862	+	7.16271i	−0.401807	+	0.291930i
$603$	−6.42302	+	19.7680i	−0.261566	+	0.805016i
$604$	8.32988	−	25.6367i	0.338938	−	1.04314i
$605$	6.19794	+	0.840035i	0.251982	+	0.0341523i
$606$	−0.508133	−	1.56387i	−0.0206415	−	0.0635279i
$607$	13.3505			0.541880			0.270940	−	0.962596i	$-0.412666\pi$
$607$	13.3505			0.541880			0.270940	+	0.962596i	$0.412666\pi$
$608$	−3.04497	−	9.37145i	−0.123490	−	0.380063i
$609$	−2.20619	−	1.60289i	−0.0893994	−	0.0649525i
$610$	9.96985	+	1.35126i	0.403667	+	0.0547109i
$611$	−12.3668	+	8.98502i	−0.500308	+	0.363495i
$612$	−3.57650	−	2.59848i	−0.144572	−	0.105037i
$613$	23.7212	+	17.2344i	0.958088	+	0.696092i	0.952706	−	0.303894i	$-0.0982868\pi$
$613$	23.7212	+	17.2344i	0.958088	+	0.696092i	0.00538228	+	0.999986i	$0.498287\pi$
$614$	4.97338	−	3.61337i	0.200709	−	0.145824i
$615$	−8.06163	−	7.70885i	−0.325076	−	0.310851i
$616$	14.7192	+	10.6941i	0.593052	+	0.430878i
$617$	0.598732	+	1.84271i	0.0241040	+	0.0741846i	0.962385	−	0.271690i	$-0.0875824\pi$
$617$	0.598732	+	1.84271i	0.0241040	+	0.0741846i	−0.938281	+	0.345874i	$0.887582\pi$
$618$	2.20161			0.0885616
$619$	−13.4373	−	41.3557i	−0.540090	−	1.66223i	−0.732387	−	0.680888i	$-0.761594\pi$
$619$	−13.4373	−	41.3557i	−0.540090	−	1.66223i	0.192298	−	0.981337i	$-0.438406\pi$
$620$	2.01879	+	11.1291i	0.0810767	+	0.446957i
$621$	1.40194	−	4.31472i	0.0562578	−	0.173144i
$622$	0.109739	−	0.337741i	0.00440012	−	0.0135422i
$623$	−38.1101	+	27.6886i	−1.52685	+	1.10932i
$624$	−16.0373			−0.642006
$625$	18.8317	−	16.4429i	0.753266	−	0.657716i
$626$	−6.72152			−0.268646
$627$	3.91060	−	2.84121i	0.156174	−	0.113467i
$628$	0.516578	−	1.58986i	0.0206137	−	0.0634424i
$629$	0.680132	−	2.09323i	0.0271186	−	0.0834626i
$630$	1.60473	+	8.84649i	0.0639338	+	0.352453i
$631$	−0.0482633	−	0.148539i	−0.00192133	−	0.00591325i	0.950091	−	0.311972i	$-0.100990\pi$
$631$	−0.0482633	−	0.148539i	−0.00192133	−	0.00591325i	−0.952013	+	0.306059i	$0.900990\pi$
$632$	10.5380			0.419179
$633$	1.39564	+	4.29533i	0.0554716	+	0.170724i
$634$	4.00205	+	2.90766i	0.158942	+	0.115478i
$635$	17.0749	+	16.3277i	0.677598	+	0.647946i
$636$	11.4690	−	8.33268i	0.454774	−	0.330412i
$637$	−50.3882	−	36.6092i	−1.99645	−	1.45051i
$638$	0.872194	+	0.633686i	0.0345305	+	0.0250879i
$639$	−1.09000	+	0.791935i	−0.0431199	+	0.0313285i
$640$	−23.4865	−	3.18324i	−0.928387	−	0.125829i
$641$	−28.8931	−	20.9921i	−1.14121	−	0.829138i	−0.153923	−	0.988083i	$-0.549191\pi$
$641$	−28.8931	−	20.9921i	−1.14121	−	0.829138i	−0.987287	+	0.158945i	$0.949191\pi$
$642$	−1.56160	−	4.80612i	−0.0616315	−	0.189682i
$643$	−29.5374			−1.16484			−0.582422	−	0.812887i	$-0.697895\pi$
$643$	−29.5374			−1.16484			−0.582422	+	0.812887i	$0.697895\pi$
$644$	2.46840	+	7.59694i	0.0972684	+	0.299361i
$645$	12.3685	+	1.67635i	0.487008	+	0.0660063i
$646$	−0.286297	+	0.881131i	−0.0112642	+	0.0346676i
$647$	0.685296	−	2.10912i	0.0269418	−	0.0829182i	−0.936682	−	0.350182i	$-0.886120\pi$
$647$	0.685296	−	2.10912i	0.0269418	−	0.0829182i	0.963623	+	0.267264i	$0.0861196\pi$
$648$	−5.33449	+	3.87573i	−0.209559	+	0.152253i
$649$	−26.7310			−1.04928
$650$	13.8098	−	5.18057i	0.541665	−	0.203199i
$651$	8.38091			0.328474
$652$	−14.6899	+	10.6729i	−0.575302	+	0.417982i
$653$	0.795100	−	2.44707i	0.0311147	−	0.0957612i	−0.934293	−	0.356506i	$-0.883968\pi$
$653$	0.795100	−	2.44707i	0.0311147	−	0.0957612i	0.965408	+	0.260745i	$0.0839680\pi$
$654$	−1.16061	+	3.57198i	−0.0453833	+	0.139675i
$655$	−14.7799	+	7.95201i	−0.577499	+	0.310711i
$656$	6.04824	+	18.6146i	0.236144	+	0.726777i
$657$	17.8999			0.698342
$658$	1.11020	+	3.41686i	0.0432803	+	0.133203i
$659$	−8.36247	−	6.07569i	−0.325756	−	0.236675i	0.412872	−	0.910789i	$-0.364526\pi$
$659$	−8.36247	−	6.07569i	−0.325756	−	0.236675i	−0.738628	+	0.674114i	$0.764526\pi$
$660$	−1.58726	−	8.75023i	−0.0617842	−	0.340602i
$661$	0.337188	−	0.244982i	0.0131151	−	0.00952868i	−0.581208	−	0.813755i	$-0.697420\pi$
$661$	0.337188	−	0.244982i	0.0131151	−	0.00952868i	0.594323	+	0.804226i	$0.297420\pi$
$662$	−5.64798	−	4.10350i	−0.219515	−	0.159487i
$663$	4.34745	+	3.15861i	0.168841	+	0.122670i
$664$	−15.7811	+	11.4656i	−0.612424	+	0.444952i
$665$	−17.3766	+	9.34908i	−0.673835	+	0.362542i
$666$	−1.80028	−	1.30798i	−0.0697596	−	0.0506833i
$667$	0.306500	+	0.943310i	0.0118677	+	0.0365251i
$668$	42.7104			1.65251
$669$	−4.46662	−	13.7468i	−0.172689	−	0.531484i
$670$	3.47772	−	7.22019i	0.134356	−	0.278940i
$671$	9.53737	−	29.3530i	0.368186	−	1.13316i
$672$	−4.15094	+	12.7753i	−0.160126	+	0.492817i
$673$	8.20262	−	5.95955i	0.316188	−	0.229724i	−0.418359	−	0.908282i	$-0.637395\pi$
$673$	8.20262	−	5.95955i	0.316188	−	0.229724i	0.734547	+	0.678558i	$0.237395\pi$
$674$	−3.07826			−0.118570
$675$	11.3610	−	17.2056i	0.437285	−	0.662245i
$676$	−67.3946			−2.59210
$677$	−33.2547	+	24.1609i	−1.27808	+	0.928581i	−0.999493	−	0.0318301i	$-0.989866\pi$
$677$	−33.2547	+	24.1609i	−1.27808	+	0.928581i	−0.278588	+	0.960411i	$0.589866\pi$
$678$	1.02070	−	3.14140i	0.0391999	−	0.120645i
$679$	−19.0208	+	58.5401i	−0.729952	+	2.24656i
$680$	2.58148	+	2.46851i	0.0989952	+	0.0946631i
$681$	−5.21440	−	16.0483i	−0.199816	−	0.614971i
$682$	−3.31330			−0.126873
$683$	4.98759	+	15.3502i	0.190845	+	0.587360i	1.00000		0.000235011i	$-7.48062e-5\pi$
$683$	4.98759	+	15.3502i	0.190845	+	0.587360i	−0.809155	+	0.587595i	$0.800075\pi$
$684$	−7.93597	−	5.76582i	−0.303440	−	0.220462i
$685$	−8.84183	+	18.3568i	−0.337829	+	0.701377i
$686$	−2.43912	+	1.77212i	−0.0931259	+	0.0676599i
$687$	16.5575	+	12.0297i	0.631709	+	0.458963i
$688$	−17.7188	−	12.8735i	−0.675523	−	0.490796i
$689$	58.3522	−	42.3954i	2.22304	−	1.61514i
$690$	−0.339036	+	0.703883i	−0.0129069	+	0.0267964i
$691$	−25.8728	−	18.7977i	−0.984249	−	0.715099i	−0.0255949	−	0.999672i	$-0.508148\pi$
$691$	−25.8728	−	18.7977i	−0.984249	−	0.715099i	−0.958654	+	0.284574i	$0.908148\pi$
$692$	1.79721	+	5.53123i	0.0683195	+	0.210266i
$693$	27.5808			1.04771
$694$	−3.13661	−	9.65350i	−0.119064	−	0.366442i
$695$	26.2241	+	25.0765i	0.994736	+	0.951205i
$696$	−0.338473	+	1.04171i	−0.0128298	+	0.0394860i
$697$	2.02663	−	6.23733i	0.0767642	−	0.236256i
$698$	−3.54621	+	2.57647i	−0.134226	+	0.0975209i
$699$	−10.6666			−0.403448
$700$	1.62334	+	36.2661i	0.0613563	+	1.37073i
$701$	−21.8973			−0.827051			−0.413525	−	0.910493i	$-0.635703\pi$
$701$	−21.8973			−0.827051			−0.413525	+	0.910493i	$0.635703\pi$
$702$	9.84112	−	7.14999i	0.371429	−	0.269859i
$703$	1.50916	−	4.64471i	0.0569190	−	0.175179i
$704$	−3.64159	+	11.2077i	−0.137248	+	0.422405i
$705$	1.59687	−	3.31532i	0.0601417	−	0.124862i
$706$	−0.757923	−	2.33265i	−0.0285248	−	0.0877903i
$707$	20.5914			0.774418
$708$	−4.00495	−	12.3260i	−0.150515	−	0.463238i
$709$	38.7104	+	28.1248i	1.45380	+	1.05625i	0.984925	+	0.172984i	$0.0553408\pi$
$709$	38.7104	+	28.1248i	1.45380	+	1.05625i	0.468876	+	0.883264i	$0.344659\pi$
$710$	0.457469	−	0.246131i	0.0171685	−	0.00923714i
$711$	12.9240	−	9.38982i	0.484687	−	0.352146i
$712$	15.3072	+	11.1213i	0.573662	+	0.416790i
$713$	−2.46610	−	1.79173i	−0.0923563	−	0.0671008i
$714$	1.02177	−	0.742363i	0.0382390	−	0.0277822i
$715$	−8.07575	−	44.5198i	−0.302016	−	1.66495i
$716$	−25.4940	−	18.5225i	−0.952757	−	0.692219i
$717$	−1.01049	−	3.10998i	−0.0377376	−	0.116144i
$718$	−11.9869			−0.447349
$719$	5.54125	+	17.0542i	0.206654	+	0.636015i	0.999641	+	0.0267774i	$0.00852453\pi$
$719$	5.54125	+	17.0542i	0.206654	+	0.636015i	−0.792988	+	0.609238i	$0.791475\pi$
$720$	−14.2303	+	7.65628i	−0.530331	+	0.285333i
$721$	−8.51947	+	26.2202i	−0.317282	+	0.976492i
$722$	1.81621	−	5.58972i	0.0675924	−	0.208028i
$723$	−13.2413	+	9.62040i	−0.492451	+	0.357787i
$724$	9.40763			0.349632
$725$	0.201569	+	4.50315i	0.00748609	+	0.167243i
$726$	−0.888319			−0.0329686
$727$	21.4696	−	15.5986i	0.796262	−	0.578518i	−0.113553	−	0.993532i	$-0.536223\pi$
$727$	21.4696	−	15.5986i	0.796262	−	0.578518i	0.909815	+	0.415014i	$0.136223\pi$
$728$	−13.8689	+	42.6840i	−0.514015	+	1.58198i
$729$	−0.181202	+	0.557681i	−0.00671117	+	0.0206548i
$730$	−6.83904	−	0.926926i	−0.253124	−	0.0343071i
$731$	2.26780	+	6.97957i	0.0838776	+	0.258149i
$732$	14.9639			0.553083
$733$	9.44110	+	29.0567i	0.348715	+	1.07323i	0.959565	+	0.281488i	$0.0908279\pi$
$733$	9.44110	+	29.0567i	0.348715	+	1.07323i	−0.610850	+	0.791747i	$0.709172\pi$
$734$	12.2382	+	8.89161i	0.451722	+	0.328195i
$735$	14.8576	+	2.01372i	0.548031	+	0.0742772i
$736$	3.95261	−	2.87174i	0.145695	−	0.105854i
$737$	−19.8892	−	14.4503i	−0.732627	−	0.532285i
$738$	−5.36442	−	3.89748i	−0.197467	−	0.143468i
$739$	−18.3281	+	13.3161i	−0.674210	+	0.489842i	−0.871432	−	0.490517i	$-0.836808\pi$
$739$	−18.3281	+	13.3161i	−0.674210	+	0.489842i	0.197222	+	0.980359i	$0.436808\pi$
$740$	−6.49384	−	6.20966i	−0.238718	−	0.228272i
$741$	9.64665	+	7.00870i	0.354378	+	0.257471i
$742$	−5.23845	−	16.1223i	−0.192309	−	0.591867i
$743$	−21.4609			−0.787326			−0.393663	−	0.919255i	$-0.628792\pi$
$743$	−21.4609			−0.787326			−0.393663	+	0.919255i	$0.628792\pi$
$744$	−1.04023	−	3.20149i	−0.0381366	−	0.117372i
$745$	6.51091	+	35.8932i	0.238541	+	1.31502i
$746$	0.595942	−	1.83412i	0.0218190	−	0.0671519i
$747$	−9.13780	+	28.1233i	−0.334335	+	1.02898i
$748$	4.23020	−	3.07342i	0.154672	−	0.112375i
$749$	63.2817			2.31226
$750$	−2.33671	+	2.67338i	−0.0853245	+	0.0976180i
$751$	−22.7580			−0.830450			−0.415225	−	0.909719i	$-0.636297\pi$
$751$	−22.7580			−0.830450			−0.415225	+	0.909719i	$0.636297\pi$
$752$	−5.22392	+	3.79540i	−0.190497	+	0.138404i
$753$	3.30841	−	10.1822i	0.120565	−	0.371061i
$754$	−0.821810	+	2.52927i	−0.0299286	+	0.0921106i
$755$	5.89278	+	32.4856i	0.214460	+	1.18227i
$756$	9.25179	+	28.4741i	0.336484	+	1.03559i
$757$	−36.2460			−1.31738			−0.658692	−	0.752413i	$-0.728890\pi$
$757$	−36.2460			−1.31738			−0.658692	+	0.752413i	$0.728890\pi$
$758$	−0.652729	−	2.00889i	−0.0237082	−	0.0729663i
$759$	1.93896	+	1.40874i	0.0703798	+	0.0511339i
$760$	5.72810	+	5.47743i	0.207780	+	0.198687i
$761$	6.43656	−	4.67643i	0.233325	−	0.169521i	−0.464979	−	0.885322i	$-0.653938\pi$
$761$	6.43656	−	4.67643i	0.233325	−	0.169521i	0.698304	+	0.715801i	$0.253938\pi$
$762$	−2.71457	−	1.97225i	−0.0983384	−	0.0714470i
$763$	−38.0496	−	27.6447i	−1.37749	−	1.00080i
$764$	1.40883	−	1.02358i	0.0509697	−	0.0370317i
$765$	5.36553	+	0.727214i	0.193991	+	0.0262925i
$766$	13.0743	+	9.49906i	0.472395	+	0.343215i
$767$	−20.3766	−	62.7126i	−0.735755	−	2.26442i
$768$	−2.89298			−0.104391
$769$	0.498848	+	1.53530i	0.0179889	+	0.0553642i	0.959648	−	0.281204i	$-0.0907337\pi$
$769$	0.498848	+	1.53530i	0.0179889	+	0.0553642i	−0.941659	+	0.336568i	$0.890734\pi$
$770$	−10.5378	−	1.42824i	−0.379757	−	0.0514702i
$771$	1.23362	−	3.79668i	0.0444276	−	0.136734i
$772$	6.46068	−	19.8839i	0.232525	−	0.715638i
$773$	11.2686	−	8.18714i	0.405304	−	0.294471i	−0.366394	−	0.930460i	$-0.619408\pi$
$773$	11.2686	−	8.18714i	0.405304	−	0.294471i	0.771698	+	0.635989i	$0.219408\pi$
$774$	7.41984			0.266701
$775$	−8.63584	−	10.8323i	−0.310209	−	0.389107i
$776$	24.7231			0.887506
$777$	−5.38609	+	3.91322i	−0.193225	+	0.140386i
$778$	−2.43600	+	7.49723i	−0.0873347	+	0.268789i
$779$	4.49693	−	13.8401i	0.161119	−	0.495874i
$780$	19.3187	−	10.3940i	0.691719	−	0.372164i
$781$	−0.492443	−	1.51558i	−0.0176210	−	0.0542318i
$782$	−0.459367			−0.0164269
$783$	1.14879	+	3.53562i	0.0410545	+	0.126353i
$784$	−21.2847	−	15.4642i	−0.760168	−	0.552295i
$785$	0.365441	+	2.01459i	0.0130431	+	0.0719039i
$786$	1.92843	−	1.40109i	0.0687849	−	0.0499752i
$787$	−4.54308	−	3.30074i	−0.161943	−	0.117659i	0.503862	−	0.863784i	$-0.331912\pi$
$787$	−4.54308	−	3.30074i	−0.161943	−	0.117659i	−0.665806	+	0.746125i	$0.731912\pi$
$788$	−9.77340	−	7.10079i	−0.348163	−	0.252955i
$789$	−7.63821	+	5.54949i	−0.271928	+	0.197567i
$790$	−5.42413	+	2.91833i	−0.192982	+	0.103830i
$791$	33.4630	+	24.3123i	1.18981	+	0.864446i
$792$	−3.42329	−	10.5358i	−0.121641	−	0.374374i
$793$	76.1342			2.70360
$794$	1.76710	+	5.43856i	0.0627119	+	0.193007i
$795$	−7.53477	+	15.6432i	−0.267231	+	0.554806i
$796$	0.451585	−	1.38984i	0.0160060	−	0.0492615i
$797$	−2.95363	+	9.09035i	−0.104623	+	0.321997i	−0.989642	−	0.143559i	$-0.954145\pi$
$797$	−2.95363	+	9.09035i	−0.104623	+	0.321997i	0.885019	+	0.465555i	$0.154145\pi$
$798$	2.26724	−	1.64724i	0.0802593	−	0.0583118i
$799$	2.16364			0.0765440
$800$	20.7892	−	7.79881i	0.735009	−	0.275730i
$801$	28.6826			1.01345
$802$	−12.4206	+	9.02408i	−0.438586	+	0.318651i
$803$	−6.54237	+	20.1354i	−0.230875	+	0.710561i
$804$	3.68334	−	11.3361i	0.129901	−	0.399795i
$805$	−7.07100	−	6.76157i	−0.249220	−	0.238314i
$806$	−2.52567	−	7.77321i	−0.0889629	−	0.273800i
$807$	−11.4197			−0.401993
$808$	−2.55578	−	7.86587i	−0.0899119	−	0.276720i
$809$	25.2788	+	18.3661i	0.888755	+	0.645718i	0.935553	−	0.353186i	$-0.114902\pi$
$809$	25.2788	+	18.3661i	0.888755	+	0.645718i	−0.0467983	+	0.998904i	$0.514902\pi$
$810$	1.67245	−	3.47222i	0.0587639	−	0.122001i
$811$	−31.9697	+	23.2273i	−1.12261	+	0.815622i	−0.984602	−	0.174809i	$-0.944069\pi$
$811$	−31.9697	+	23.2273i	−1.12261	+	0.815622i	−0.138005	+	0.990431i	$0.544069\pi$
$812$	−5.29546	−	3.84737i	−0.185834	−	0.135016i
$813$	14.7664	+	10.7284i	0.517880	+	0.376262i
$814$	2.12933	−	1.54705i	0.0746331	−	0.0542241i
$815$	9.65087	−	20.0364i	0.338055	−	0.701846i
$816$	1.83643	+	1.33424i	0.0642877	+	0.0467078i
$817$	5.03206	+	15.4871i	0.176050	+	0.541825i
$818$	1.20120			0.0419990
$819$	21.0243	+	64.7062i	0.734649	+	2.26102i
$820$	−19.3501	−	18.5033i	−0.675734	−	0.646164i
$821$	−4.38345	+	13.4909i	−0.152983	+	0.470834i	−0.997951	−	0.0639832i	$-0.979620\pi$
$821$	−4.38345	+	13.4909i	−0.152983	+	0.470834i	0.844968	+	0.534817i	$0.179620\pi$
$822$	0.894238	−	2.75218i	0.0311901	−	0.0959934i
$823$	−41.2914	+	30.0000i	−1.43933	+	1.04573i	−0.451146	+	0.892450i	$0.648985\pi$
$823$	−41.2914	+	30.0000i	−1.43933	+	1.04573i	−0.988182	+	0.153283i	$0.951015\pi$
$824$	11.0735			0.385764
$825$	6.78989	+	8.51683i	0.236393	+	0.296518i
$826$	−15.4978			−0.539236
$827$	−19.1539	+	13.9161i	−0.666045	+	0.483910i	−0.868699	−	0.495340i	$-0.835043\pi$
$827$	−19.1539	+	13.9161i	−0.666045	+	0.483910i	0.202654	+	0.979250i	$0.435043\pi$
$828$	1.50297	−	4.62567i	0.0522319	−	0.160753i
$829$	−9.96765	+	30.6773i	−0.346191	+	1.06547i	0.614752	+	0.788720i	$0.289256\pi$
$829$	−9.96765	+	30.6773i	−0.346191	+	1.06547i	−0.960943	+	0.276746i	$0.910744\pi$
$830$	4.94763	−	10.2719i	0.171735	−	0.356543i
$831$	−0.494680	−	1.52247i	−0.0171603	−	0.0528139i
$832$	−29.0698			−1.00781
$833$	2.72419	+	8.38421i	0.0943877	+	0.290496i
$834$	−4.16910	−	3.02903i	−0.144364	−	0.104887i
$835$	−46.0671	+	24.7854i	−1.59422	+	0.857734i
$836$	9.38648	−	6.81968i	0.324638	−	0.235863i
$837$	−9.24320	−	6.71558i	−0.319492	−	0.232124i
$838$	5.76074	+	4.18543i	0.199002	+	0.144583i
$839$	29.4448	−	21.3929i	1.01655	−	0.738565i	0.0509752	−	0.998700i	$-0.483767\pi$
$839$	29.4448	−	21.3929i	1.01655	−	0.738565i	0.965572	+	0.260135i	$0.0837671\pi$
$840$	−1.92836	−	10.6306i	−0.0665349	−	0.366792i
$841$	22.8040	+	16.5680i	0.786343	+	0.571312i
$842$	−4.77870	−	14.7073i	−0.164685	−	0.506848i
$843$	17.8770			0.615716
$844$	3.34990	+	10.3099i	0.115308	+	0.354883i
$845$	72.6913	−	39.1100i	2.50066	−	1.34542i
$846$	0.675988	−	2.08048i	0.0232410	−	0.0715283i
$847$	3.43749	−	10.5795i	0.118114	−	0.363516i
$848$	24.6488	−	17.9084i	0.846444	−	0.614977i
$849$	3.04637			0.104551
$850$	−2.01236	−	0.555695i	−0.0690233	−	0.0190602i
$851$	2.42147			0.0830068
$852$	0.625073	−	0.454142i	0.0214146	−	0.0155587i
$853$	12.4807	−	38.4118i	0.427332	−	1.31519i	−0.473411	−	0.880842i	$-0.656977\pi$
$853$	12.4807	−	38.4118i	0.427332	−	1.31519i	0.900743	−	0.434352i	$-0.143023\pi$
$854$	5.52946	−	17.0179i	0.189214	−	0.582341i
$855$	11.9057	+	1.61363i	0.407165	+	0.0551850i
$856$	−7.85446	−	24.1735i	−0.268460	−	0.826234i
$857$	41.0814			1.40331			0.701656	−	0.712516i	$-0.252444\pi$
$857$	41.0814			1.40331			0.701656	+	0.712516i	$0.252444\pi$
$858$	1.98579	+	6.11165i	0.0677939	+	0.208648i
$859$	−14.8855	−	10.8150i	−0.507888	−	0.369002i	0.304134	−	0.952629i	$-0.401633\pi$
$859$	−14.8855	−	10.8150i	−0.507888	−	0.369002i	−0.812022	+	0.583627i	$0.801633\pi$
$860$	29.6876	+	4.02370i	1.01234	+	0.137207i
$861$	−16.0493	+	11.6605i	−0.546958	+	0.397388i
$862$	8.47208	+	6.15532i	0.288560	+	0.209651i
$863$	24.3469	+	17.6891i	0.828779	+	0.602143i	0.919214	−	0.393759i	$-0.128826\pi$
$863$	24.3469	+	17.6891i	0.828779	+	0.602143i	−0.0904344	+	0.995902i	$0.528826\pi$
$864$	14.8148	−	10.7636i	0.504009	−	0.366184i
$865$	−5.14830	−	4.92301i	−0.175047	−	0.167387i
$866$	5.18696	+	3.76855i	0.176260	+	0.128061i
$867$	−0.235041	−	0.723382i	−0.00798241	−	0.0245673i
$868$	20.1164			0.682796
$869$	5.83880	+	17.9700i	0.198068	+	0.609590i
$870$	−0.114266	−	0.629925i	−0.00387400	−	0.0213565i
$871$	18.7402	−	57.6765i	0.634989	−	1.95429i
$872$	−5.83755	+	17.9661i	−0.197684	+	0.608410i
$873$	30.3208	−	22.0293i	1.02620	−	0.745580i
$874$	−1.01930			−0.0344783
$875$	−22.7966	−	38.1743i	−0.770665	−	1.29053i
$876$	−10.2649			−0.346817
$877$	−7.96160	+	5.78444i	−0.268844	+	0.195327i	−0.714037	−	0.700108i	$-0.753135\pi$
$877$	−7.96160	+	5.78444i	−0.268844	+	0.195327i	0.445193	+	0.895435i	$0.353135\pi$
$878$	4.13660	−	12.7312i	0.139604	−	0.429656i
$879$	−2.37914	+	7.32225i	−0.0802465	+	0.246973i
$880$	−3.41131	−	18.8058i	−0.114995	−	0.633943i
$881$	7.59492	+	23.3748i	0.255879	+	0.787516i	0.993655	+	0.112470i	$0.0358762\pi$
$881$	7.59492	+	23.3748i	0.255879	+	0.787516i	−0.737776	+	0.675046i	$0.764124\pi$
$882$	8.91308			0.300119
$883$	−8.62117	−	26.5332i	−0.290125	−	0.892914i	−0.984815	−	0.173605i	$-0.944458\pi$
$883$	−8.62117	−	26.5332i	−0.290125	−	0.892914i	0.694690	−	0.719309i	$-0.255542\pi$
$884$	10.4351	+	7.58151i	0.350969	+	0.254994i
$885$	11.4726	+	10.9706i	0.385648	+	0.368772i
$886$	3.30670	−	2.40246i	0.111091	−	0.0807122i
$887$	4.01332	+	2.91585i	0.134754	+	0.0979046i	0.653120	−	0.757254i	$-0.273460\pi$
$887$	4.01332	+	2.91585i	0.134754	+	0.0979046i	−0.518366	+	0.855159i	$0.673460\pi$
$888$	2.16336	+	1.57177i	0.0725977	+	0.0527453i
$889$	33.9931	−	24.6974i	1.14009	−	0.828326i
$890$	−10.9588	−	1.48530i	−0.367340	−	0.0497873i
$891$	−9.56480	−	6.94924i	−0.320433	−	0.232808i
$892$	−10.7211	−	32.9961i	−0.358969	−	1.10479i
$893$	4.80094			0.160657
$894$	−1.60101	−	4.92739i	−0.0535456	−	0.164797i
$895$	38.2466	+	5.18373i	1.27844	+	0.173273i
$896$	−13.0261	+	40.0901i	−0.435170	+	1.33932i
$897$	−1.82695	+	5.62278i	−0.0610001	+	0.187739i
$898$	9.38373	−	6.81768i	0.313139	−	0.227509i
$899$	2.49785			0.0833080
$900$	12.1798	−	18.4456i	0.405992	−	0.614854i
$901$	−10.2090			−0.340112
$902$	6.34490	−	4.60984i	0.211262	−	0.153491i
$903$	6.85977	−	21.1122i	0.228279	−	0.702570i
$904$	5.13388	−	15.8004i	0.170750	−	0.525515i
$905$	−10.1470	+	5.45937i	−0.337298	+	0.181476i
$906$	−1.44901	−	4.45959i	−0.0481401	−	0.148160i
$907$	−9.56996			−0.317765			−0.158883	−	0.987297i	$-0.550789\pi$
$907$	−9.56996			−0.317765			−0.158883	+	0.987297i	$0.550789\pi$
$908$	−12.5160	−	38.5202i	−0.415357	−	1.27834i
$909$	−10.1433	−	7.36953i	−0.336432	−	0.244432i
$910$	−4.68206	−	25.8111i	−0.155209	−	0.855631i
$911$	−14.5603	+	10.5787i	−0.482403	+	0.350487i	−0.802255	−	0.596981i	$-0.796367\pi$
$911$	−14.5603	+	10.5787i	−0.482403	+	0.350487i	0.319852	+	0.947467i	$0.396367\pi$
$912$	4.07488	+	2.96057i	0.134933	+	0.0980344i
$913$	−28.2956	−	20.5580i	−0.936449	−	0.680370i
$914$	5.27437	−	3.83206i	0.174461	−	0.126753i
$915$	−16.1400	+	8.68377i	−0.533572	+	0.287077i
$916$	39.7425	+	28.8746i	1.31313	+	0.954044i
$917$	9.22401	+	28.3886i	0.304604	+	0.937473i
$918$	−1.72175			−0.0568263
$919$	−7.36300	−	22.6610i	−0.242883	−	0.747517i	−0.995977	−	0.0896045i	$-0.971440\pi$
$919$	−7.36300	−	22.6610i	−0.242883	−	0.747517i	0.753094	−	0.657912i	$-0.228560\pi$
$920$	−1.70527	+	3.54035i	−0.0562209	+	0.116722i
$921$	−3.46055	+	10.6505i	−0.114029	+	0.350945i
$922$	0.348700	−	1.07319i	0.0114838	−	0.0353435i
$923$	3.18027	−	2.31060i	0.104680	−	0.0760544i
$924$	−15.8164			−0.520322
$925$	10.6078	+	2.92924i	0.348781	+	0.0963129i
$926$	3.64610			0.119818
$927$	13.5808	−	9.86699i	0.446050	−	0.324075i
$928$	−1.23715	+	3.80755i	−0.0406114	+	0.124989i
$929$	−9.04193	+	27.8282i	−0.296656	+	0.913013i	0.686004	+	0.727598i	$0.259363\pi$
$929$	−9.04193	+	27.8282i	−0.296656	+	0.913013i	−0.982660	+	0.185416i	$0.940637\pi$
$930$	1.42203	+	1.35980i	0.0466302	+	0.0445897i
$931$	6.04477	+	18.6039i	0.198109	+	0.609718i
$932$	−25.6027			−0.838646
$933$	0.199907	+	0.615251i	0.00654467	+	0.0201424i
$934$	8.72090	+	6.33611i	0.285357	+	0.207324i
$935$	−2.77912	+	5.76981i	−0.0908870	+	0.188693i
$936$	22.1082	−	16.0625i	0.722628	−	0.525020i
$937$	−32.8252	−	23.8489i	−1.07235	−	0.779110i	−0.0960192	−	0.995379i	$-0.530611\pi$
$937$	−32.8252	−	23.8489i	−1.07235	−	0.779110i	−0.976334	+	0.216269i	$0.930611\pi$
$938$	−11.5311	−	8.37783i	−0.376504	−	0.273546i
$939$	9.90590	−	7.19705i	0.323267	−	0.234867i
$940$	3.83293	−	7.95765i	0.125016	−	0.259550i
$941$	−46.1996	−	33.5660i	−1.50607	−	1.09422i	−0.967886	−	0.251390i	$-0.919112\pi$
$941$	−46.1996	−	33.5660i	−1.50607	−	1.09422i	−0.538179	−	0.842830i	$-0.680888\pi$
$942$	−0.0898604	−	0.276562i	−0.00292781	−	0.00901087i
$943$	7.21539			0.234966
$944$	−8.60735	−	26.4907i	−0.280145	−	0.862199i
$945$	−26.5028	−	25.3430i	−0.862136	−	0.824409i
$946$	−2.71194	+	8.34648i	−0.0881726	+	0.271367i
$947$	−11.9572	+	36.8004i	−0.388556	+	1.19585i	0.545312	+	0.838233i	$0.316411\pi$
$947$	−11.9572	+	36.8004i	−0.388556	+	1.19585i	−0.933868	+	0.357619i	$0.883589\pi$
$948$	−7.41137	+	5.38468i	−0.240710	+	0.174886i
$949$	−52.2260			−1.69533
$950$	−4.46526	−	1.23304i	−0.144872	−	0.0400052i
$951$	−9.01144			−0.292216
$952$	5.13926	−	3.73389i	0.166564	−	0.121016i
$953$	−2.53251	+	7.79426i	−0.0820360	+	0.252481i	−0.983659	−	0.180042i	$-0.942377\pi$
$953$	−2.53251	+	7.79426i	−0.0820360	+	0.252481i	0.901623	+	0.432523i	$0.142377\pi$
$954$	−3.18962	+	9.81663i	−0.103268	+	0.317825i
$955$	−0.925561	+	1.92158i	−0.0299505	+	0.0621810i
$956$	−2.42546	−	7.46480i	−0.0784450	−	0.241429i
$957$	−1.96392			−0.0634846
$958$	3.69084	+	11.3592i	0.119246	+	0.367000i
$959$	29.3169	+	21.3000i	0.946694	+	0.687813i
$960$	6.16263	−	3.31567i	0.198898	−	0.107013i
$961$	18.8690	−	13.7091i	0.608677	−	0.442230i
$962$	5.25263	+	3.81626i	0.169352	+	0.123041i
$963$	−31.1725	−	22.6482i	−1.00452	−	0.729827i
$964$	−31.7828	+	23.0915i	−1.02365	+	0.743729i
$965$	4.57046	+	25.1959i	0.147128	+	0.811085i
$966$	1.12415	+	0.816740i	0.0361688	+	0.0262782i
$967$	15.5807	+	47.9525i	0.501042	+	1.54205i	0.807324	+	0.590108i	$0.200915\pi$
$967$	15.5807	+	47.9525i	0.501042	+	1.54205i	−0.306283	+	0.951941i	$0.599085\pi$
$968$	−4.46801			−0.143607
$969$	−0.521537	−	1.60513i	−0.0167542	−	0.0515641i
$970$	−12.7255	+	6.84666i	−0.408591	+	0.219833i
$971$	−0.780757	+	2.40292i	−0.0250557	+	0.0771134i	−0.962802	−	0.270206i	$-0.912908\pi$
$971$	−0.780757	+	2.40292i	−0.0250557	+	0.0771134i	0.937747	+	0.347320i	$0.112908\pi$
$972$	8.75050	−	26.9313i	0.280672	−	0.863821i
$973$	52.2074	−	37.9309i	1.67369	−	1.21601i
$974$	−8.52011			−0.273002
$975$	−14.8052	+	22.4217i	−0.474146	+	0.718070i
$976$	32.1602			1.02942
$977$	−8.64076	+	6.27788i	−0.276442	+	0.200847i	−0.717364	−	0.696698i	$-0.754652\pi$
$977$	−8.64076	+	6.27788i	−0.276442	+	0.200847i	0.440922	+	0.897546i	$0.354652\pi$
$978$	−0.976062	+	3.00401i	−0.0312110	+	0.0960576i
$979$	−10.4834	+	32.2647i	−0.335052	+	1.03118i
$980$	35.6623	+	4.83347i	1.13919	+	0.154399i
$981$	8.84935	+	27.2355i	0.282538	+	0.869562i
$982$	6.31218			0.201430
$983$	−3.43941	−	10.5854i	−0.109700	−	0.337622i	0.881105	−	0.472921i	$-0.156800\pi$
$983$	−3.43941	−	10.5854i	−0.109700	−	0.337622i	−0.990805	+	0.135299i	$0.956800\pi$
$984$	6.44630	+	4.68351i	0.205501	+	0.149305i
$985$	14.6622	+	1.98723i	0.467177	+	0.0633185i
$986$	0.304530	−	0.221254i	0.00969823	−	0.00704617i
$987$	−5.29477	−	3.84688i	−0.168534	−	0.122447i
$988$	23.1545	+	16.8228i	0.736644	+	0.535203i
$989$	−6.53202	+	4.74579i	−0.207706	+	0.150907i
$990$	4.67977	+	4.47498i	0.148733	+	0.142224i
$991$	5.12727	+	3.72518i	0.162873	+	0.118334i	0.666236	−	0.745741i	$-0.267904\pi$
$991$	5.12727	+	3.72518i	0.162873	+	0.118334i	−0.503363	+	0.864075i	$0.667904\pi$
$992$	−3.80213	−	11.7018i	−0.120718	−	0.371531i
$993$	12.7176			0.403580
$994$	−0.285502	−	0.878685i	−0.00905558	−	0.0278702i
$995$	0.319463	+	1.76113i	0.0101277	+	0.0558316i
$996$	5.24015	−	16.1275i	0.166041	−	0.511021i
$997$	11.7853	−	36.2716i	0.373246	−	1.14873i	−0.571409	−	0.820665i	$-0.693603\pi$
$997$	11.7853	−	36.2716i	0.373246	−	1.14873i	0.944655	−	0.328066i	$-0.106397\pi$
$998$	10.8341	−	7.87144i	0.342948	−	0.249166i
$999$	9.07590			0.287149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.11	✓	76
25.16	even	5	inner	425.2.k.b.341.11	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.11	✓	76	1.1	even	1	trivial
425.2.k.b.341.11	yes	76	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.337793 - 0.245421i) q^{2} +(-0.235041 + 0.723382i) q^{3} +(-0.564161 + 1.73631i) q^{4} +(-0.399103 - 2.20016i) q^{5} +(0.0981377 + 0.302037i) q^{6} -3.97689 q^{7} +(0.493607 + 1.51917i) q^{8} +(1.95901 + 1.42331i) q^{9} +(-0.674779 - 0.645251i) q^{10} +(-2.31708 + 1.68345i) q^{11} +(-1.12341 - 0.816208i) q^{12} +(-5.71575 - 4.15274i) q^{13} +(-1.34336 + 0.976012i) q^{14} +(1.68536 + 0.228425i) q^{15} +(-2.41442 - 1.75418i) q^{16} +(0.309017 + 0.951057i) q^{17} +1.01105 q^{18} +(0.685684 + 2.11032i) q^{19} +(4.04532 + 0.548281i) q^{20} +(0.934733 - 2.87681i) q^{21} +(-0.369536 + 1.13732i) q^{22} +(-0.890072 + 0.646675i) q^{23} -1.21496 q^{24} +(-4.68143 + 1.75618i) q^{25} -2.94991 q^{26} +(-3.33608 + 2.42380i) q^{27} +(2.24361 - 6.90512i) q^{28} +(0.278588 - 0.857407i) q^{29} +(0.625363 - 0.336463i) q^{30} +(0.856186 + 2.63507i) q^{31} -4.44078 q^{32} +(-0.673172 - 2.07181i) q^{33} +(0.337793 + 0.245421i) q^{34} +(1.58719 + 8.74981i) q^{35} +(-3.57650 + 2.59848i) q^{36} +(-1.78061 - 1.29369i) q^{37} +(0.749535 + 0.544569i) q^{38} +(4.34745 - 3.15861i) q^{39} +(3.14542 - 1.69232i) q^{40} +(-5.30579 - 3.85488i) q^{41} +(-0.390283 - 1.20117i) q^{42} +7.33875 q^{43} +(-1.61579 - 4.97290i) q^{44} +(2.34966 - 4.87820i) q^{45} +(-0.141952 + 0.436884i) q^{46} +(0.668601 - 2.05774i) q^{47} +(1.83643 - 1.33424i) q^{48} +8.81568 q^{49} +(-1.15035 + 1.74215i) q^{50} -0.760608 q^{51} +(10.4351 - 7.58151i) q^{52} +(-3.15476 + 9.70935i) q^{53} +(-0.532051 + 1.63748i) q^{54} +(4.62862 + 4.42607i) q^{55} +(-1.96302 - 6.04157i) q^{56} -1.68773 q^{57} +(-0.116320 - 0.357997i) q^{58} +(7.55075 + 5.48594i) q^{59} +(-1.34743 + 2.79744i) q^{60} +(-8.71809 + 6.33406i) q^{61} +(0.935914 + 0.679981i) q^{62} +(-7.79079 - 5.66034i) q^{63} +(3.32877 - 2.41849i) q^{64} +(-6.85553 + 14.2330i) q^{65} +(-0.735857 - 0.534632i) q^{66} +(2.65252 + 8.16363i) q^{67} -1.82566 q^{68} +(-0.258590 - 0.795857i) q^{69} +(2.68352 + 2.56609i) q^{70} +(-0.171939 + 0.529172i) q^{71} +(-1.19526 + 3.67863i) q^{72} +(5.98037 - 4.34500i) q^{73} -0.918974 q^{74} +(-0.170061 - 3.79924i) q^{75} -4.05100 q^{76} +(9.21476 - 6.69491i) q^{77} +(0.693349 - 2.13391i) q^{78} +(2.03864 - 6.27430i) q^{79} +(-2.89587 + 6.01220i) q^{80} +(1.27561 + 3.92593i) q^{81} -2.73832 q^{82} +(3.77365 + 11.6141i) q^{83} +(4.46770 + 3.24597i) q^{84} +(1.96915 - 1.05946i) q^{85} +(2.47898 - 1.80108i) q^{86} +(0.554753 + 0.403052i) q^{87} +(-3.70117 - 2.68906i) q^{88} +(9.58289 - 6.96238i) q^{89} +(-0.403512 - 2.22447i) q^{90} +(22.7309 + 16.5150i) q^{91} +(-0.620685 - 1.91027i) q^{92} -2.10740 q^{93} +(-0.279164 - 0.859178i) q^{94} +(4.36939 - 2.35085i) q^{95} +(1.04376 - 3.21238i) q^{96} +(4.78283 - 14.7201i) q^{97} +(2.97787 - 2.16355i) q^{98} -6.93525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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